Bernoulli Bibliography

B


Back to Index       Back to A       On to C


BABADGANJAN R.S.,
[1] Ob ostatochnom chlene v formule Ejlera-Maklorena (Russian) [On the remainder term in the Euler-Maclaurin formula]. Leningr. Gos. Pedagog. In-t., Leningrad, 1986, 14 str.
R1986,7A18DEP

[2] K istorii odnogo funktsional'nogo uravneniya Ejlera (Russian) [On the history of a functional equation of Euler]. Leningr. Gos. Pedagog. In-t., Leningrad, 1986, 6 str.
R1986,7A19DEP

BABBAGE CH.,
[1] On some new methods of investigating the sums of several classes of infinite series, Philos. Trans. Roy. Soc. London 109 (1819), 249-282.

BABINI J.,
[1] Polinomios generalizades de Bernoulli y sus correlativos, Boletén Sem. mat. Argentino, 4 (1934), 23-25. and Rev. mat. hisp-amer. (2), 10 (1934), 23-25.
J61.1166.03; J60.1041.04; Z11.21301

[2] Generalización de los polinomios de Bernoulli, Rev. Acad. Sci. Madrid, 32 (1935), 491-500.
J61.0378.01; Z13.16703

BACHMANN P.,
[1] Niedere Zahlentheorie, Additive Zahlentheorie, Leipzig, 1910 / New York: Chelsea, 1968, Part 1: x+402p; Part II: x+480p.
J41.0221.10; Z253.10001; M39#25

[2] Das Fermatproblem in seiner bisherigen Entwicklung, Walter de Gruyter & Co., Berlin-Leipzig, 1916, 160pp.
J47.0105.02

[3] Ein Satz von den Tangentenkoeffizienten, Arch. der Math. u. Physik (3), 16 (1910), 363-365.
J41.0223.01

BAILEY D.H., BORWEIN J.M., CRANDALL R.E.,
[1] On the Khintchine constant. Math. Comp., 66 (1997), no. 217, 417-431.
Z854.11078; M97c:11119

BAILEY D.H., BORWEIN J.M., GIRGENSOHN R.,
[1] Experimental evaluation of Euler sums. Experiment. Math., 3 (1994), no. 1, 17-30.
Z810.11076; M96e:11168

BAKER Alan,
[1] A Concise Introduction to the Theory of Numbers, Cambridge University Press, Cambridge, 1984. xiii + 95 pp.
Z554.10001; M86f:11001

BAKER A.J., CLARKE F., RAY N., SCHWARTZ L.,
[1] On the Kummer congruences and the stable homotopy of BU, Trans. Amer. Math. Soc., 316 (1989), no. 2, 385-432.
Z709.55012; M90c:55003; R1990,12A606

BAKER Andrew,
[1] A supersingular congruence for modular forms, Acta Arith. 86 (1998), no. 1, 91-100.
M99j:11066; R01.02-13A.299

BAKHMUTSKAYA E.Ya.,
[1] Dzhon Blissard i ego simvolicheskoye ischisleniye [John Blissard and his symbolic calculus], Trudy XIII mezhdunarodnogo kongressa po istorii nauki, sek. 5, 1971, 121-124. Nauka, Moskva, 1974.
Z296.01015; R1975,1A44

BALAN G.,
[1] Group of unit of cyclotomic field, In: Proc. Conference on Algebra. Univ. of Cluj-Napoca, Faculty of Math., Research Seminars. Preprint No. 9, 1986, 3-6.
Z691.12001; R1987,5A317

BALANZARIO E.P.,
[1] Evaluation of Dirichlet Series. Amer. Math. Monthly 108 (2001), no. 10, 969-971

BALATONI F.,
[1] Valós kvadraticus számtestek osztályszámáról [On the class number of quadratic number fields] (Hungarian), Math. Lapok, 24 (1973), 107-112.
Z326.12004 ; M53#5527; R1976,6A179

BALAZS N.L., SCHMIT C., VOROS A.,
[1] Spectral fluctuations and zeta functions, J. Statistical Physics, 46 (1987), no. 5/6, 1067-1090.
Z692.58027; M89b:58171

BALK M.B.,
[1] A property of the Bernoulli numbers. (Russian), Moskov. Oblast. Pedagog. Inst. Uch. Zap., 57 (1957), 55-59.
Z90.27901; M20#5892; R1958,7462

BALOG A., DARMON H., ONO K.,
[1] Congruence for Fourier coefficients of half-integral weight modular forms and special values of $L$-functions. Analytic number theory, Vol. 1 (Allerton Park, IL, 1995), 105-128, Progr. Math., 138, Birkhäuser Boston, Boston, MA, 1996.
Z863.11031; M97e:11056

BAMBAH R.P.,
[1] Chowla, the mathematics man. Math. Student 67 (1998), no. 1-4, 153-161.

BANASZAK G., GAJDA W.,
[1] On the arithmetic of cyclotomic fields and the $K$-theory of ${\bf Q}$, Algebraic $K$-theory Poznan, 1995), 7-18, Contemp. Math., 199, Amer. Math. Soc., Providence, RI, 1996.
Z866.19004; M97h:11146

BANERJEE D.P.,
[1] On some arithmetical properties of Bernoulli's and Euler's generalized polynomials, Proc. Indian Nat. Sci. Acad. Part A, 34 (1964), 92-96.
Z171.32601; M36#2851; R1965,6V50

BANKS W.,
[1] Some unusual identities for special values of the Riemann zeta function. Ramanujan J. 5 (2001), no. 2, 153-157.
Z1031.11048; M2002f:11112

BANUELOS A., DEPINE R.A.,
[1] A program for computing the Riemann zeta function for complex argument, Comput. Phys. Comm., 20 (1980), 441-445.
Z457.10001; R1981,5V1033

BARANIECKI M.A.,
[1] Ueber die Bernoulli'schen Functionen. [On the Bernoulli functions]. Kraków, Ak. (Mat.-Przyrod.) Rozpr. 13 (1885), 183-195.
J17.0416.03

BARNER K.,
[1] Über die Werte der Ringklassen-L-Funktionen reell-quadratischer Zahlkörper an natürlichen Argumentstellen, J. Number Theory, 1 (1969), no. 1, 28-64.
Z174.08604; M39#139; R1970,2A127

BARNES E. W.,
[1] The theory of the gamma function, Messenger Math. (2), 29 (1899/1900), 64-128.
J30.0389.01

[2] The theory of the double gamma function, Philos. Trans. London, 196A (1901), 271-285.
J32.0442.02

[3] On the theory of the multiple gamma function, Trans. Cambr. Philos. Soc., 19 (1904), 374-425.
J35.0462.01

BARNIVILLE J.J., DICKSON J.D.H., LAMPE E.,
[1] Solution of question 9977, Math. questions etc., edited by W.J.C. Miller, London, 52 (1890), 41-44.
J22.0268.03

BARSKY D.,
[1] Analyse p-adique et nombres de Bernoulli, C.R. Acad. Sci. Paris, 283 (1976), no. 16, A1069-A1072.
Z359.12018 ; M55#2855; R1977,7A339

[2] Congruences de coefficients de séries de Taylor (Application aux nombres de Bernoulli-Hurwitz), Groupe d'étude d'analyse ultramétrique, no. 17, (1975-76), 9pp.
Z355.12016; M58#5496; R1978,3A300

[3] Fonction génératrice et congruences (Application aux nombres de Bernoulli), Sém. Delange-Pisot-Poitou (Théorie de nombres), 1975-76 (1977), 17, fasc. 1, exp. 21, 16pp.
Z336.12012 ; M57#5967; R1978,3A235

[4] Analyse p-adique et nombres de Bernoulli-Hurwitz, C.R. Acad. Sci. Paris, 284 (1977), no. 3, A137-A140.
Z343.12007; M55#12705; R1977,10A208

BARSKY D., DUMONT D.,
[1] Congruences pour les nombres de Genocchi de deuxième espèce, Seminaire du groupe d'étude d'analyse ultramétrique, 34 (1980-81), 1-13.
Z474.10011; M82m:10021; R1982,1V747

BARTZ K.,
[1] On Carlitz theorem for Bernoulli polynomials. Number theory (Cieszyn, 1998). Ann. Math. Sil. No. 12 (1998), 9-13.
Z924.11009; M2000a:11030

BARTZ K., RUTKOWSKI J.,
[1] On the von Staudt-Clausen theorem, C. R. Math. Rep. Acad. Sci. Canada, 15 (1993), no. 1, 46-48.
Z769.11011; M94b:11017; R1993,11A101

BASKOV B.M.,
[1] Svyaz' dzeta-funktsii Rimana s mnogochlenami Bernulli (Russian) [Connection between the Riemann zeta function and the Bernoulli polynomials]. Trudy Uzbeksk. Gos. Universiteta, novaya ser., fiz.-mat. fakul't., Samarkand, (1958), no. 78, 163-183.
R1962,5A127

[2] Novoe dokazatel'stvo teoremy Shtaudta (Russian) [A new proof of Staudt's theorem]. Materialy 3-i ob'ed. nauch. konf. uchenykh Samarkanda, ser. gumanit. i estest. nauk, Samarkand, (1961), 260-262.
R1963,3A140

BATEN W. D.,
[1] A remainder for the Euler-Maclaurin summation formula in two independent variables, Amer. J. Math., 54 (1932), 265-275.
J58.1044.08; Z4.25001

BAUER G.,
[1] Von den Gamma-functionen und einer besonderen Art unendlicher Producte, J. Reine Angew. Math., 57 (1860) , 256-272.

[2] Von einigen Summen-und Differenzenformeln und den Bernoullischen Zahlen, J. Reine Angew. Math., 58 (1861), 292-300.

Bayad, Abdelmejid,
[1] Applications aux sommes elliptiques d'Apostol-Dedekind-Zagier. (French) [Applications to elliptic Apostol-Dedekind-Zagier sums] C. R. Math. Acad. Sci. Paris 339 (2004), no. 8, 529-532.
M2005k:11094

BAYAT M.,
[1] A generalization of Wolstenholme's theorem, Amer. Math. Monthly 104 (1997), no. 6, 557-560.
Z916.11002; M98e:11007

BÁYER P.,
[1] Value of the Iwasawa L-function at point $s=1$, Arch. Math., 32 (1979), no. 1, 38-54.
Z403.12022; M80h:12016 ; R1980,2A374

[2] Sobre el indice de irregularidad de los numeros primos, Collect. Math., 30 (1979), no. 1, 11-20, (Spanish).
Z499.12003; M81h:12003

[3] Variae observationes circa series infinititas, Butlleti Soc. Catalana Ciénc. Fis., Quimiques i Matem., 2 (1984), no. 4, 429-481.
Z598.10002; M86i:01026

BEACH B., WILLIAMS H., ZARNKE C.,
[1] Some computer results on units in quadratic and cubic fields, Proc. of the Twenty-Fifth Summer Meeting of the Canad. Math. Congress, Lakehead Univ., (1971), 609-648.
M49#2656

BEARDON A. F.,
[1] Sums of powers of integers. Amer. Math. Monthly, 103 (1996), no. 3,201-213 .
Z851.11012; M97f:11020; R1996,10B189

BEAUPAIN J.,
[1] Sur une classe de fonctions qui se rattachent aux fonctions de Jacques Bernoulli. Mémoires Couronnés et Mémoires des Savants Étrangers publiés par l'Académie Royale des Sciences, des Lettres et des Beaux-Arts de Belgique, Bruxelles, 59 (1901), pt. 1, 33 pp.
J34.0483.01

BECK M.,
[1] Dedekind cotangent sums. Acta Arith. 109 (2003), no. 2, 109-130.

BEEBEE J.,
[1] Bernoulli numbers and exact covering systems, Amer. Math. Monthly, 99 (1992), no. 10, 946-948.
Z776.11008; M93i:11025; R1993,8A109

BEEGER N.W.G.H.,
[1] Quelques remarques sur les congruences $\tau^{p-1 \equiv 1 (\bmod p^2)$ et $(p - 1)! \equiv (\bmod p^2)$, Messeng. Math. (2), 43 (1913), 72-84.
J44.0227.01

[2] On some new congruences in the theory of Bernoulli numbers, Bull. Amer. Math. Soc., 44 (1938), 684-688.
J64.0096.01; Z19.29201

[3] Report on some calculations of prime numbers, Nieuw Arch. Wisk., 20 (1939), 48-50.
J65.0161.02; Z20.10506; M1-65g

BEESLEY E.M.,
[1] An integral representation for the Euler numbers, Amer. Math. Monthly, 76 (1969), 389-391.
Z185.03002; M39#4330; R1970,3V274

BELL E.T.,
[1] The Bernoullian functions occuring in the arithmetical applications of elliptic functions, Messeng. Math. (2), 50 (1921), 177-186. = Bull Amer. Math. Soc., 27 (1921), 413.
J48.0444.04; J48.1245.04

[2] Note on the prime divisors of the numerator of Bernoulli's numbers, Amer. Math. Monthly, 28 (1921), 258-259. = Bull. Amer. Math. Soc., 27 (1921), 414.
J48.0137.01; J48.0255.18

[3] An harmonic polynomial generalizations of the numbers of Bernoulli and Euler, Bull. Amer. Math. Soc., 27 (1921), 414.
J48.0255.19

[4] An harmonic polynomial generalizations of the numbers of Bernoulli and Euler, Trans. Amer. Math. Soc., 24 (1922), no. 2, 89-112.
J49.0708.01

[5] A revision of the Bernoullian and Eulerian functions, Bull. Amer. Math. Soc., 28 (1922), 443-450.
J48.1194.03

[6] Relations between the numbers of Bernoulli, Euler, Genocchi, and Lucas, Messeng. Math., 52 (1923), 56-68.
J49.0328.01

[7] Umbral symmetric functions and algebraic analogues of the Bernoullian and Eulerian numbers and functions, Bull. Amer. Math. Soc., 29 (1923), 11. = Math. Z., 19 (1924), 35-49.
J49.0078.04; J49.0250.02

[8] An algebra of sequences of functions with an application to the Bernoulli functions, Trans. Amer. Math. Soc., 28 (1926), no. 1, 129-148.
J52.0372.03

[9] General relations between Bernoulli, Euler and allied polynomials, Trans. Amer. Math. Soc., 38 (1935), 493-500.
J61.0377.04; Z13.00503

[10] The history of Blissard's symbolic method, with a sketch of its inventor's life, Amer. Math. Monthly, 45 (1938), 414-421.
Z19.38902

[11] Trigonometry and the numbers B, E, G, R of Bernoulli, Euler, Genocchi and Lucas (Abstract), Bull. Amer. Math. Soc., 28 (1922), 283.
J48.0256.02

[12] The modular Bernoullian and Eulerian functions (Abstract ), Bull. Amer. Math. Soc., 32 (1926), 417-418.
J52.0373.02

[13] On generalizations of the Bernoullian functions and numbers, Amer. J. Math., 47 (1926), 277-288.
J51.0289.01

[14] $B, E$ polynomials and their related integrals, Tôhoku Math. J, 26 (1926), 391-405.
J52.0354.01

[15] Modular Bernoullian and Eulerian functions, Univ. of Washington Publ. in Math., 1 (1926), no. 1, 1-7.
J57.1369.02

BELL J.L.,
[1] Chains of congruences for the numerators and denominators of the Bernoulli numbers, Ann. of Math. (2), 29 (1927), 106-112.
J53.0137.02

BELLAVITIS G.,
[1] Sulle serie di numeri che comprendono i Bernoulliani, Annali. sci. mat. e fis. Roma, 4 (1853), 108-127.

BENCZE M., SMARANDACHE F.,
[1] About Bernoulli's numbers. Octogon Math. Mag. 7 (1999), no. 1, 151-153.

BENDERSKI L.,
[1] Sur la fonction gamma géneralisée, Acta Math. 61 (1933), 263-322.

BENNETON G.,
[1] Sur le dernier théorème de Fermat, Ann. Sci. Univ. Besançon, Math. (3), fasc. 7 (1974), 15pp.
Z348.10010; M54#7368

BENTSEN S., MADSEN I.,
[1] Trace maps in algebraic $K$-theory and the Coates-Wiles homomorphism, J. Reine Angew. Math., 411 (1990), 171-195.
Z716.11055; M91i:19002

BERG F.J. van den,
[1] Over periodieke terugloopende betrekkingen tusschen de Coëfficiënten in de ontwikkeling van functiën, meer in het byzonder tusschen de Bernoulliaansche en ook tusschen eenige daarmede verwante Coëfficiënten, Versl. Meed. Kon. Ak. Weten., (2), 16 (1881), 74-176 = Arch. Néerl. Sci. Ex. Nat. Soc. Holland., 16 (1881), 387-443.
J13.0193.01

[2] Eenige formulen voor de berekening van de Bernoulliaansche en van de tangenten-coëfficiënten, Verhand. Kgl. Akad. Wetensch. Amsterdam, (3), 5 (1889), 388-397; 6 (1889), 265-276.
J20.0265.02

[3] Nogmaals over de Bernoulliaansche coëfficienten. Amst. Versl. en Meded. (3) 6 (1889), 265-276.
J21.0248.02

[4] Quelques formules pour le calcul des nombres de Bernoulli et des coefficients des tangentes, Arch. Néerl. Sci. Exactes et Natur. Soc. Hollandaise, 24 (1891), 99-141.
J22.0268.02

BERG L.,
[1] On the solution of Jordan's system of difference equations. Rostock. Math. Kolloq. No. 56 (2002), 25-28.
M2003f:39010; R02.12-13B.272

[2] On polynomials related with generalized Bernoulli numbers. Rostock. Math. Kolloq. No. 56 (2002), 55-61.
M2003d:11027

BERGER A.,
[1] Elementära bevis för några formler i differenskalkylen, Handl. Kgl. Svenska Vetens. Akad., Stockholm, 37 (1882), 39-53.
J14.0192.01

[2] De Bernoulli'ska talens och funktionernas teori, baserad på ett system af funktionaleqvationer, Öfversigt af Kgl. Svenska Vetens. Akad. Förhand., Stockholm, 45 (1888), 433-461.
J20.0424.02

[3] Härledning af några independenta uttryck för de Bernoulli'ska talen, Öfversigt af Kgl. Svenska Vetens. Akad. Förhand., Stockholm, 46 (1889), 129-138.
J1.0247.02

[4] Sur une généralisation des nombres et des fonctions de Bernoulli, Bihang Kgl. Svenska Vetens. Akad. handl., Stockholm, 13 (1890), no. 9, 1-43.
J20.0266.01

[5] Recherches sur les nombres et les fonctions de Bernoulli, Acta Math., 14 (1890/91), 249-304.
J23.0267.02

[6] Om en användning af de Bernoulliska funktionerna vid några serienutvecklingar, Öfversigt af Kgl. Svenska Vetens. Akad. Förhandl., Stockholm, 48 (1891), 523-540.
J23.0274.02

BERGER E.R.,
[1] Bernoullische Zahlen, Potenzsummen und Stirlingsche Reihe, Z. Angew. Math. Mech., 35 (1955), no. 1/2, 70-71.
Z64.01308; M16-1014e; R1956,2302

BERGGREN B.,
[1] Summierung der Reihe $1^n + 2^n + 3^n + \cdots + \nu^n$ (Swedish), Elementa, Stockholm, 22 (1939), 209-212.
J65.1190.03

BERGMANN H.,
[1] Eine explizite Darstellung der Bernoullischen Zahlen, Math. Nachr., 34 (1967), 377-378.
Z307.10018 ; M36#4030; R1968,6V311

BERNARDINI A.: see NATALINI P., BERNARDINI A.

BERNDT B.C.,
[1] Character transformation formulae similar to those for the Dedekind eta-function. In: Analytic number theory (Proc. Sympos. Pure Math., Vol. 24, St. Louis Univ., St. Louis, Mo., 1972), pp. 9-30. Amer. Math. Soc., Providence, R. I., 1973.
Z265.10016; M49#2556

[2] Periodic Bernoulli numbers, summation formulas and applications. In: Theory and application of special functions (Proc. Advanced Sem., Math. Res. Center, Univ. Wisconsin, Madison, Wis., 1975), pp. 143-189. Math. Res. Center, Univ. Wisconsin, Publ. No. 35, Academic Press, New York, 1975.
Z326.10016; M52#10560; R1978,7B39

[3] Elementary evaluation of $\zeta(2n)$, Math. Mag., 48 (1975), 148-154.
Z303.10038; M51#3078; R1976,5A98

[4] Character analogues of the Poisson and Euler-Maclaurin summation formulas with applications, J. Number Theory, 7 (1975), no. 4, 413-445.
Z316.10023; M52#3075; R1976,6A131

[5] On Eisenstein series with characters and the values of Dirichlet L-functions, Acta Arith., 28 (1975), no. 3, 299-320.
Z279.10023; M52#10601; R1976,8A177

[6] Dedekind sums and a paper of G.H. Hardy, J. London Math. Soc., 13 (1976), 129-137.
Z319.10006; M53#7918; R1976,12A127

[7] Chapter 8 of Ramanujan's second notebook, J. Reine Angew. Math., 338 (1983), 1-55.
Z491.33003; M84g:01080; R1983,7B13

[8] Chapter 11 of Ramanujan's second notebook, Bull. London Math. Soc., 15 (1983), no. 4, 273-320.
Z494.33002; M85a:01043; R1983,12B35

[9] Ramanujan's quarterly reports, Bull. London Math. Soc., 16 (1983), no. 5, 449-489.
Z511.01007; M85j:01021; R1985,4A101

[10] Remarks on some of Ramanujan's number theoretical discoveries found in his second notebook. Number Theory. Proc. 4th Matscience Conf. held at Ootacamund, India, January 5-10, 1984. Lect. Notes Math. No. 1122, Springer-Verlag Berlin-New York, 1985, 47-55.
Z555.10002; M87b:11013; R1985,11A121

[11] Ramanujan's Notebooks. Part I. Springer-Verlag, New York-Berlin, 1985, x + 357 pp.
Z555.10001; M86c:01062; R1986,2B1K

[12] Ramanujan's notebooks. Part IV. Springer-Verlag, New York, 1994. xii+451pp.
Z785.11001; M95e:11028

[13] Ramanujan's notebooks. Part V. Springer-Verlag, New York, 1998. xiv+624pp.
Z886.11001; M99f:11024

[14] The evaluation of certain classes of nonabsolutely convergent double series. SIAM J. Math. Anal. 6 (1975), no. 6, 966-977.
Z0311.40002; M52 #1085; R1976,5A123

BERNDT B.C., BIALEK P.,
[1] Five formulas of Ramanujan arising from Eisenstein series. In: Number Teory (K. Dilcher, Ed.), Fourth Conference of the Canadian Number Theory Association (Halifax, July 2-8, 1994), CMS Conference Proceedings 15, 67-86. Amer. Math. Soc., Providence, 1995.
Z838.40001; M97f:11028; R1997,9A122

BERNDT B.C., EVANS R.J.,
[1] Chapter 7 of Ramanujan's second notebook, Proc. Indian Acad. Sci. Math. Sci., 92 (1983), no. 2, 67-96.
Z537.10002; M86d:11020; R1985,3A95

[2] Extensions of asymptotic expansions from Chapter 15 of Ramanujan's second notebook, J. Reine Angew. Math., 361 (1985), 118-134.
Z571.41027; M87b:41031; R1986,4A125

[3] Chapter 15 of Ramanujan's second notebook. Part II. Modular forms. Acta Arith., 47 (1986), no. 2, 123-142.
Z571.10025; M88d:11039; R1987,5A96

[4] Asymptotic expansion of a series of Ramanujan, Proc. Edinburgh Math. Soc.(2), 35 (1992), no. 2, 189-199.
Z741.41025; M93i:41020

BERNDT B.C., EVANS R.J., WILSON B.M.,
[1] Chapter 3 of Ramanujan's second notebook, Advances in Math., 49 (1983), no. 2, 123-169.
Z524.41017; M85c:11020; R1984,2B41

BERNDT B.C., SCHOENFELD L.,
[1] Periodic analogues of the Euler-Maclaurin and Poisson summation formulas with applications to number theory, Acta Arith., 28 (1975), 23-68. Correction: Acta Arith., 38 (1980/81), 328.
Z268.10008; M52#5586; R1976,5A106

BERNDT B.C., WILSON B.M.,
[1] Chapter 5 of Ramanujan's second notebook. In: Analytic number theory, Lecture Notes in Math., no. 899, Springer-Verlag, 1981, 49-78.
Z477.10003; M83i:10011

BERNDT B.C.: see also ADIGA C., BERNDT B.C., et al.

BERNOULLI J.,
[1] Ars Conjectandi, Basel, (1713). (Reprinted on pp. 106-286 in Vol. 3 of "Die Werke von Jakob Bernoulli", Birkhäuser Verlag, Basel, 1975. See also SMITH D.E. [1, pp. 85-90]).

[2] Wahrscheinlichkeitsrechnung, Leipzig, 1899.

BERNSTEIN F.,
[1] Über den zweiten Fall des letzten Fermatschen Lehrsatzes, Nachr. Akad. Wiss. Göttingen Math.-phys. Kl., (1910), 507-516.
J41.0237.01

BERNSTEIN M., SLOANE N.J.A.,
[1] Some canonical sequences of integers, Linear Algebra Appl., 226-228 (1995), 57-72.
Z832.05002; M96i:05004

BERTRAND J.,
[1] Traité de calcul différentiel et de calcul intégral, Paris, 1 (1864), Ch. 6; 2 (1870), Ch. 7. 507-616.
J02.0298.01

BESSEL F.W.,
[1] Über die Summation der Progressionen, Astronom. Nachr., 16 (1839), no. 361, 1-6.

BEUKERS F., KOLK J.A.C., CALABI E.,
[1] Sums of generalized harmonic series and volumes, Nieuw Arch. Wisk. (4), 11 (1993), no. 3, 217-224.
Z797.40001; M94j:11022

BEZERRA V.B., CHABA A.N.,
[1] The generalised Euler formula from Poisson's summation formula and some applications, J. Phys. A 18 (1985), no. 17, 3381-3387.
Z596.40002; M87h:65013; R1986,6B17

BHARGAVA S.: see ADIGA C., BERNDT, B.C. et al.

BHARGAVA S.: see ADIGA C., BHARGAVA S.

BHATTACHARJEE N.R.,
[1] Extension of Bernoulli and Euler numbers (Bengali summary), Chittagong Univ. Stud. Part II Sci., 10 (1986), no. 1-2, 13-17.
M90d:11030

BHATTACHARJEE N.R., BHATTACHARJEE T.,
[1] Extension of zeta function $\zeta(2m)$, Indian J. Pure Appl. Math., 21 (1990), no. 11, 977-980.
Z721.11032; M92d:11091

[2] On the evaluation of zeta function $\zeta(2s)$, Indian J. Pure Appl. Math., 23 (1992), no. 1, 15-19.
Z742.11043; M93b:11105; R1992,9A144

BHIMASENA RAO M.: see KRISHNAMACHARY C., BHIMASENA RAO M.

BIALEK P.: see BERNDT B.C., BIALEK P.

BILU Yu. F., BRINDZA B., KIRSCHENHOFER P., Pintér Á., TICHY R. F.,
[1] Diophantine equations and Bernoulli polynomials. With an appendix by A. Schinzel. Compositio Math. 131 (2002), no. 2, 173-188.
M2003a:11025; R02.11-13A.79

BINET M.J.,
[1] Mémoires sur les intégrales définies Euleriennes, Journ. de l'Ecole Polytechn., 16 (1839), 124-343.

[2] Mémoire sur l'application de la théorie des suites à la série des nombres premiers à un nombre composé, C.R. Acad. Sci. Paris, 32 (1851), 918-921.

BIRCH B.J.,
[1] $K_2$ of Global fields, Proc. Sympos. Pure Math., 20 (1971), 87-95.
Z218.12010; M48#11052

BISHT C.S.: see SRIVASTAVA H.M., JOSHI J.M.C., BISHT C.S.

BJÖRLING E.G.,
[1] Om de Bernoulliska talen, Öfversigt Kgl. Vetens. Akad. Förhandl., Stockholm, 14 (1857), 107-108.

BLIND A.,
[1] Ueber die Potenzsummen der unter einer Zahl m liegenden und zu ihr primen Zahlen, Dissertation, Bonn 1876 .

BLISSARD J.,
[1] Theory of generic equations, Quart. J. Math., 4 (1861), 279-305; [2] Examples of the use and application of representative notation, Quart. J. Math., 6 (1863), 49-64.

[3] Researches in analysis. I. On the sums of reciprocals, Quart. J. Math., 6 (1864), 242-257.

[4] Researches in analysis. II. On the unlimited variety of result capable of being obtained, by use of Representative Notation, from a single Formula, Quart. J. Pure Appl. Math., 7 (1866), 155-170, 223-226.

[5] On the properties of the $\bigtriangleup^m \bigcirc^n$ class of numbers and of others analogous to them, as investigated by means of representative notation, Quart. J. Math., 8 (1867), 85-110.

[6] Note on a certain formula, Quart. J. Pure Appl. Math. 9 (1868), 71-76.

[7] On the properties of the $\bigtriangleup^m \bigcirc^n$ class of numbers, Quart. J. Pure Appl. Math., 9 (1868), 82-94, 154--171.

BLOOM D. M.,
[1] An old algorithm for the sums of integer powers. Math. Magazine, 66 (1993), no. 5, 304-305.
M94j:11017

BOCK W.,
[1] Eine Beziehung zwischen den Bernoullischen Zahlen und dem Produkt $\Pi (1-1/p^{2n})$ über alle Primzahlen, Mitt. Math. Ges. Hamburg, 5 (1920), 304-307.
J47.0219.04

BÖCHERER S.,
[1] Über die Fourierkoeffizienten der Siegelschen Eisensteinreihen, Manuscripta Math., 45 (1984), no. 3, 273-288.
Z533.10023; M86b:11037; R1984,9A445

BÖCHERER S., SCHMIDT C.-G.,
[1] $p$-adic measures attached to Siegel modular forms. Ann. Inst. Fourier (Grenoble) 50 (2000), no. 5, 1375-1443.

Z0962.11023; M2001k:11082

BÖHMER P.,
[1] Über die Bernoullischen Functionen, Math. Ann., 68 (1910), no. 3, 338-360.
J41.0371.02

BÖLLING R.,
[1] Bemerkungen über Klassenzahlen und Summen von Jacobi-Symbolen, Math. Nachr., 90 (1979), 159-172.
Z415.12003; M81g:12008; R1980,5A149

BOOLE G.,
[1] Die Grundlehren der endlichen Differenzen- und Summenrechnung. Leibrock, Braunschweig, 1867.

[2] Finite differences, Chapters V-VIII, (1872).

[3] A treatise of the calculus of finite differences, London, (1880), 3rd. ed., Ch. 5-8.

BOREVICH Z.I., SHAFAREVICH I.R.,
[1] Number Theory. Academic Press, New York, 1966. x + 435 pp.
Z121.04202; M33#4001

[2] Teoriya chisel [Number Theory], 3rd ed., Nauka, Moscow, 1985, 504 pp.
Z592.12001; M88f:11001; R1986,1A533K

BORWEIN D., BORWEIN J.M., BORWEIN P.B., GIRGENSOHN R.,
[1] Giuga's conjecture on primality, Amer. Math. Monthly 103 (1996), no. 1, 40-50.
Z860.11003; M97b:11004; R1997,12A58

BORWEIN J.M., BORWEIN P.B.,
[1] Pi and the AGM. A study in analytic number theory and computational complexity. John Wiley & Sons, Inc., New York, 1987.
Z611.10001; M89a:11134

BORWEIN J.M., BORWEIN P.B., DILCHER K.,
[1] Pi, Euler numbers, and asymptotic expansions, Amer. Math. Monthly, 96 (1989), no.8, 681-687.
Z711.11009; M91c:40002

[2] Boole summation and asymptotic expansions of some special series. Conference report of the 9th Czechoslovak Colloquium on Number Theory held at Rackova Dolina, Sept. 1989, pp. 11-18. Masaryk University, Brno, 1990.

BORWEIN J.M., BROADHURST D.J., KAMNITZER J.,
[1] Central binomial sums, multiple Clausen values, and zeta values. Experiment. Math. 10 (2001), no. 1, 25-34.

BORWEIN J.M., WONG E.,
[1] A survey of results relating to Giuga's conjecture on primality. Advances in mathematical sciences: CRM's 25 years Montreal, PQ, 1994), 13--27, CRM Proc. Lecture Notes, 11, Amer. Math. Soc., Providence, RI, 1997.
Z980.15140; M98i:11005

BORWEIN J.M.: see also BAILEY D.H., BORWEIN J.M., GIRGENSOHN R.

BORWEIN J.M.: see also BAILEY D.H., BORWEIN J.M., CRANDALL R.E.

BORWEIN J.M.: see also BORWEIN D., BORWEIN J.M., BORWEIN P.B., GIRGENSOHN R.

BORWEIN P.B.: see BORWEIN J.M., BORWEIN P.B.

BORWEIN P.B.: see also BORWEIN J.M., BORWEIN P.B., DILCHER K.

BORWEIN P.B.: see also BORWEIN D., BORWEIN J.M., BORWEIN P.B., G IRGENSOHN R.

BOWMAN D., BRADLEY D. M.,
[1] Multiple polylogarithms: a brief survey. In: $q$-series with applications to combinatorics, number theory, and physics (Urbana, IL, 2000), 71--92, Contemp. Math., 291, Amer. Math. Soc., Providence, RI, 2001.

Z0998.33013; M2003c:33021; R02.10-13A.74

BOYD, D.W.,
[1] A $p$-adic study of the partial sums of the harmonic series, Experiment. Math. 3 (1994), no. 4, 287-302.
Z838.11015; M96e:11157

BOYER C. B.,
[1] Pascal's formula for the sum of powers of the integers, Scripta Math., 9 (1943), 237-244.
Z60.00919; M6-85d

BOYLAN M.,
[1] Swinnerton-Dyer type congruences for certain Eisenstein series. $q$-series with applications to combinatorics, number theory, and physics (Urbana, IL, 2000), 93-108, Contemp. Math., 291, Amer. Math. Soc., Providence, RI, 2001.
Z0990.11028; M2002k:11063; R02.11-13A.79

BRADLEY D.,
[1] A sieve auxiliary function. Analytic number theory, Vol. 1 (Allerton Park, IL, 1995), 173-210, Progr. Math., 138, Birkhäuser Boston, Boston, MA, 1996.
Z856.11045; M97h:11099

BRADLEY D.: see also BOWMAN D., BRADLEY D. M.

BREMEKAMP H.,
[1] Vraagstuk CXIII, Wiskundige Opgaven, 14 (1928), 238-240.
J54.0186.01

BRENEV E.E.,
[1] O nekotorykh sootnosheniyakh svyazyvayushchikh dzeta-funktsiyu Rimana s polinomami Bernulli [On some relations between the Riemann zeta function and Bernoulli polynomials]. Trudy Moskovsk. instituta inzhenerov zh.-d. transporta, (1966), no. 230, 77-98.< br> R1967,11A141

BRENT B.,
[1] Quadratic minima and modular forms, Experiment. Math. 7 (1998), no. 3, 257-274.
Z916.11025; M2000f:11048

BRESSOUD D.M.,
[1] A radical approach to real analysis. Mathematical Association of America, Washington, DC, 1994. xii+324 pp.
Z796.26001; M95d:26002

BRETTI G, RICCI P.E.,
[1] Euler polynomials and the related quadrature rule. Georgian Math. J. 8 (2001), no. 3, 447--453.
Z0992.33004; M2003d:65018

Bretti, Gabriella; Ricci, Paolo E.,
[2] Multidimensional extensions of the Bernoulli and Appell polynomials. Taiwanese J. Math. 8 (2004), no. 3, 415-428.

BRETTI G., NATALINI P., RICCI P.E.,
[1] Generalizations of the Bernoulli and Appell polynomials. Abstr. Appl. Anal. 2004, no. 7, 613-623.

BRILLHART J.,
[1] On the Euler and Bernoulli polynomials, J. Reine Angew. Math., 234 (1969), 45-64.
Z167.35401; M39#4117; R1969,8B176

[2] Some modular results on the Euler and Bernoulli polynomials, Acta Arith., 21 (1972), 173-181.
Z213.05503; M46#3433; R1973,4A194

[3] On the Euler and Bernoulli polynomials. Dissertation, Univ. of California, Berkeley, 1967.
R1986,7V288D

BRINDZA B.,
[1] On some generalizations of the Diophantine equation $1^k+2^k+ \cdots +x^k = y^z$, Acta Arith., 44 (1984), no. 2, 99-107.
Z497.10010; M86j:11029; R1985,7A188

[2] Power values of sums $1^k+2^k+ \cdots +x^k$, Number Theory, Vol. II (Budapest, 1987), 595-611, Colloq. Math. Soc. Jànos Bolyai, 51, Noth-Holland, Amsterdam-New York, 1990.
Z705.11013; M91g:11027; R1992,6A143

BRINDZA B., PINTÉR Á.,
[1] On equal values of power sums, Acta Arith., 77 (1996), no. 1, 97-101.
Z960.51219; M97e:11040; R1997,3A54

BRINDZA B.: see also BILU Yu. F., BRINDZA B., KIRSCHENHOFER P., Pintér Á., TICHY R. F.

BRINKLEY J.,
[1] An investigation on the general term of an important series in the inverse method of finite differences, Phil. Trans. Royal Soc. London 97 (1807), part 1, 114-132.

BRIOSCHI F.,
[1] Sulle funzioni Bernoulliane ed Euleriane. Annali di Matematica Pura et Applicata, 1 (1858), 260-263.

BROADHURST D.J.: see BORWEIN J.M., BROADHURST D.J., KAMNITZER J.

BROCARD H.,
[1] Solutions des questions proposées (138, 139), Nouv. Corres. Math., 5 (1879), 282-285.

BRÖDEL W.,
[1] Zum von-Staudtschen Primzahlsatz, Wiss. Z. Friedrich-Schiller-Univ. Jena, Math.-Nat. Reihe, 10 (1960-61), no. 1-2, 21-23.
M23#A3701; R1962,1A143

BROOKE M.,
[1] Fibonacci formulas. Fibonacci Quart. 1 (1963), 60.

BRUCKMAN P.S.,
[1] The generalized totient function (Problem #6446, solution by O.P. Lossers), Amer. Math. Monthly, 92 (1985), no. 6, 434-435.
Z679.10011; R1987,11A91

BRÜCKNER H.,
[1] Explizites Reziprozitätsgesetz und Anwendungen, Vorlesungen Fachbereich Math. Univ. Essen, Heft 2, (1979), 83pp.
Z437.12001; M80m:12015

BRUGGEMAN R.W.,
[1] Automorphic forms. In: Elementary and analytic theory of numbers (Warsaw, 1982), 31-74, Banach Center Publ., 17, PWN, Warsaw, 1985.
Z589.10028; M87h:11037

BRUMER A.,
[1] Travaux récent D'Iwasawa et de Leopoldt, Séminaire Bourbaki, 19e année, 325 (1966/67) (1968), 1-14.
Z191.33501

BRUN V., JACOBSTHAL E., SELBERG A., SIEGEL C.,
[1] En brevveksling om et polynom som er i slekt med Riemanns zetafunksjon [Correspondence about a polynomial which is related to Riemann's zeta function], Norsk Mat. Tidsskr. 28, (1946). 65-71.
Z063.00643; M87h:11037

DE BRUYN G.F.C.,
[1] Formulas for $a+a^2 2^p+a^3 3^p+\cdots+a^n n^p$. Fibonacci Quart. 33 (1995), no. 2, 98-103.
Z827.05003; M96e:11026

DE BRUYN G.F.C., DE VILLIERS J.M.,
[1] Formulas for $1+2^p+3^p+\ldots +n^p$. Fibonacci Quart., 32 (1994), no.3, 271-276.
Z803.11017; M95f:11012

BUCHHEIM A.,
[1] Some applications of symbolic methods. Messenger of Math. 11 (1882), 143-145.

BUCKHOLTZ T.J.: see KNUTH D.E., BUCKHOLTZ T.J.

BUDMANI P.,
[1] Über die Bernoullischen Zahlen (Croatian), Arbeiten der südslavischen Akademie von Agram, Kroatien, 183 (1910), 177-199.
J41.0302.07

BUGAEV N.V.,
[1] Uchenie o chislovykh proizvodnykh [Studies on numerical derivatives](Russian). Mat. Sbornik, I, 5 (1870), 1-63; 6 (1872/73), 133-180, 201-254, 309-360.
J03.0075.03

[2] Svojstva odnogo chislovago integrala po delitelyam i ego razlichnye primeneniya, logarifmicheskie chislovye funktsii [A property of a numerical integral with regard to divisors and its various applications] (Russian). Mat. Sbornik, I, 13 (1888), 757-777.
J20.0186.01

BUHLER J.P., CRANDALL R.E., ERNVALL R., METSÄNKYLÄ T.,
[1] Irregular primes and cyclotomic invariants to four million. Math. Comp., 61 (1993), no. 203, 151-153.
Z789.11020; M93k:11014

BUHLER J.P., CRANDALL R.E., ERNVALL R., METSÄNKYLÄ T., SHOKROLLAHI M. A.,
[1] Irregular primes and cyclotomic invariants to 12 million. Computational algebra and number theory (Milwaukee, WI, 1996). J. Symbolic Comput. 31 (2001), no. 1-2, 89-96.
Z1001.11061; M2001m:11220; R02.09-13A.86

BUHLER J.P., CRANDALL R.E., SOMPOLSKI R.W.,
[1] Irregular primes to one million. Math. Comp. 59 (1992), no. 200, 717-722.
Z768.11009; M93a:11106; R1994,2A84

BUHLER J.P., GROSS B.H.,
[1] Arithmetic on elliptic curves with complex multiplication, II, Invent. Math., 79 (1985), no. 1, 11-29.
Z584.14027; M86j#11066; R1985,7A478

BUHLER J.P.: see also CRANDALL R.E., BUHLER J.P.

BUKHSHTABER V.M.,
[1] O $J$-funktorye kletochnykh kompleksov [The $J$-functor on cellular complexes] (Russian), Dokl. Akad. Nauk SSSR., 170 (1966), no. 1, 17-20.
Z153.25102; M36#3346; R1967,1A341

BÜLOW T.,
[1] The negative Pell equation. C. R. Math. Acad. Sci. Soc. R. Can. 24 (2002), no. 2, 55-60.
M2003b:11018

BUNDSCHUH P., JI CHUN-GANG, SHAN ZUN,
[1] A remarkable class of congruences. Acta Sci. Math. (Szeged) 67 (2001), no. 3-4, 493-500.
Z0997.11006; M2003a:11003

BURAU W.,
[1] Staudt, K. G. Ch. In: Dictionary of Scientific Biography (Ch. C. Gillespie, Edit. in Chief), Council of Learned Societies, Ch. Scribner's Son, New York, 1976. Vol. 13, 4-6.

BURROWS B.L., TALBOT R.F.,
[1] Sums of powers of integers, Amer. Math. Monthly, 91 (1984), no. 7, 394-403.
Z553.05006; M85j:11018; R1985,5A116

BURSTALL F.W.,
[1] Congrunces se rapportant aux nombres de Bernoulli et d'Euler au module $p^{i+1}$, J. Math. Pures Appl. (7), 3 (1917), 247-261.
J46.0189.02

BUSK Th.,
[1] On some general types of polynomials in one, two or n variables, Ejnar Munksgaard, Copenhagen, 1955, 228p.
Z068.25103

BUTZER P.L., FLOCKE S., HAUSS M.,
[1] Euler functions $E_\alpha(z)$ with complex $\alpha$ and applications. In: Approximation, probability and related fields (Santa Barbara, CA, 1993), 127-150, Plenum, New York, 1994.
M96b:33013

BUTZER P.L., HAUSS M.,
[1] On Stirling functions of the second kind, Stud. Appl. Math., 84 (1991), no. 1, 71-91.
Z738.11025; M92k:11023

BUTZER P.L., HAUSS M., LECLERC M.,
[1] Bernoulli numbers and polynomials of arbitrary complex indices, Appl. Math. Lett., 5 (1992), no. 6, 83-88.
Z768.11010; M96c:11023

[2] Extensions of Euler polynomials to Euler functions $E_\alpha(z)$ with complex indices. Pre-print, Lehrstuhl A für Mathematik, RWTH Aachen, 1992.

BUTZER P.L., MARKETT C., SCHMIDT M.,
[1] Stirling numbers, central factorial numbers, and representations of the Riemann zeta-function, Resultate Math., 19 (1991), no. 3-4, 257-274.
Z724.11038; M92a:11095

Butzer, P. L.; Pogány, Tibor K.; Srivastava, H. M.,
[1] A linear ODE for the Omega function associated with the Euler function $E\sb \alpha(z)$ and the Bernoulli function $B\sb \alpha(z)$. Appl. Math. Lett. 19 (2006), no. 10, 1073--1077.

BUTZER P.L., SCHMIDT M.,
[1] Central factorial numbers and their role in finite difference calculus and approximation, In: Colloq. Math. Soc. János Bolyai, 58 (1990), (Proc. Conf. on Approximation Theory, Kecskemét, Hungary, Aug. 5-11, 1990), 127-150.
Z784.41028; M94c:41007; R1997,2A84

BUTZER P.L., SCHMIDT M., STARK E.L., VOGT L.,
[1] Central factorial numbers; their main properties and some applications, Numer. Funct. Anal. Optim., 10 (1989), no. 5-6, 419-488.
Z659.10012; M90d:05007; R1990,2V334

BYEON D.,
[1] Special values of zeta functions of the simplest cubic fields and their applications. Proc. Japan Acad. Ser. A Math. Sci. 74 (1998), no. 1, 13-15.
Z908.11052; M99c:11141

[2] Existence of certain fundamental discriminants and class numbers of real quadratic fields. J. Number Theory 98 (2003), no. 2, 432-437.
M2003k:11169

BYKOVSKII V.A.,
[1] Pairwise products of Eisenstein series, and Manin theta functions. (Russian) Dokl. Akad. Nauk 375 (2000), no. 2, 154-156.
M2002h:11043

BYRD P.F.,
[1] New relations between Fibonacci and Bernoulli numbers, Fibonacci Quart., 13 (1975), 59-69.
Z297.10007; M51#12684; R1975,10V245

[2] Relations between Euler and Lucas numbers, Fibonacci Quart., 13 (1975), no. 2, 111-114.
Z301.10013; M50#9771; R1975,11V322


Back to Index       Back to A       On to C