Bernoulli Bibliography

D


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DABROWSKI A.,
[1] A note on $p$-adic $q$-$\zeta$-functions, J. Number Theory 64 (1997), no. 1, 100-103.
Z876.11055; M98c:11128

DAHLGREN T.,
[1] Sur le théorème de condensation de Cauchy. Dissertation, Lund, 1918. 69pp. (Ch. 1: Sur les nombers et les polynomes de Bernoulli doubles et multiples.)
J46.0326.02

D'ALMEIDA AREZ, J. B.: see d'ALMEIDA AREZ, J. B.

DAMAMME G.,
[1] Transcendence properties of Carlitz zeta-values. The Arithmetic of Function Fields (Proceedings, Ohio State Univ., 1991), 303-311. Walter deGruyter, Berlin - New York 1992.
Z788.11021; M94a:11109

DAMIANOU P., SCHUMER P.,
[1] A theorem involving the denominator of Bernoulli numbers. Math. Mag. 76 (2003), 219-224.

DANG SI SHAN, CHU WEI PAN,
[1] Some identities involving Euler numbers, Bernoulli numbers, and generalized Stirling numbers of the first kind. (Chinese), Pure Appl. Math. 13 (1997), no. 2, 109-113, 117.
Z899.11007; M99d:11018

D'ANIELLO C.,
[1] On some inequalities for the Bernoulli numbers, Rend. Circ. Mat. Palermo (2), 43 (1994), no. 3, 329-332.
Z830.11108; M96f:11030

DARBOUX G.,
[1] Sur les développements en série des fonctions d'une seule variable, J. Math. Pures Appl. (3), 2 (1876), 291-312.
J08.0124.03

DARMON H., DIAMOND F., TAYLOR R.,
[1] Fermat's last theorem. Elliptic curves, modular forms & Fermat's last theorem (Hong Kong, 1993), 2-140, Internat. Press, Cambridge, MA, 1997.
M99d:11067b

DARMON H.: see also BALOG A., DARMON H., ONO K.

DATTOLI G., LORENZUTTA S., CESARANO C.,
[1] Finite sums and generalized forms of Bernoulli polynomials. Rend. Mat. Appl. (7) 19 (1999), no. 3, 385-391 (2000).
Z958.33006; M2001h:33007

DAVID E.,
[1] Applications de la dérivation d'Arbogast à la solution de la partition des nombres et à d'autres problèmes, J. Math. Pures Appl., 8, (1882), 61-72.
J14.0129.01

DAVIS B.: see SITARAMACHANDRA RAO R., DAVIS B.

DAVIS H.T.,
[1] Tables of the Higher Mathematical Functions, v.2, Bloomington, Indiana: Principia Press, 1935, xiii + 391pp.
J61.1337.03; Z13.21603

DEBNATH L.: see LUO QIU-MING, GUO BAI-NI, QI FENG, DEBNATH L.

DEBNATH L.: see also LUO QIU-MING, QI FENG, DEBNATH L.

DEEBA E.Y., RODRIGUEZ D.M.,
[1] Stirling's series and Bernoulli numbers, Amer. Math. Monthly, 98 (1991), no.5, 423-426.
Z743.11012; M92g:11025; R1992,453

DELABAERE E.: see CANDELPERGHER B., COPPO M.A., DELABAERE E.,

DELANGE H.,
[1] Sur les zéros réels des polynômes de Bernoulli, C.R. Acad. Sci. Paris, 303, Série I, (1986), no. 12, 539-542.
Z607.10006; M88a:11020; R1987,3B31

[2] Sur les zéros imaginaires des polynômes de Bernoulli, C.R. Acad.Sci. Paris, 304, Série I, (1987), no. 6, 147-150.
Z607.10007; M88d:30009; R1987,7B20

[3] On the real roots of Euler polynomials, Monatsh. Math., 106 (1988), no. 2, 115-138.
Z653.10010; M89k:11009; R1989,3A250

[4] Sur les zéros réels des polynômes de Bernoulli, Ann. Inst. Fourier, Grenoble, 41 (1991), no. 2, 267-309.
Z725.11011; M93h:11023; R1992,6B16

DELIGNE P., RIBET K.A.,
[1] Values of Abelian L-functions at negative integers over totally real fields, Invent. Math., 59 (1980), no. 3, 227-286.
Z434.12009; M81m:12019; R1982,3A341

DELL'ACCIO F.: see COSTABILE F.A., DELL'ACCIO F.

DELVOS F.-J.,
[1] Bernoulli functions and periodic B-splines, Computing, 38 (1987), no. 1, 23-31.
Z616.65147; M88f:41017; R1987,11B1272

DEMAILLY J.P.,
[1] Sur le calcul numérique de la constante d'Euler, Gaz. Math., no. 27 (1985), 113-126.
M86m:11105

DE MOIVRE A.,
[1] Miscellanea analytica de seriebus et quadraturis, London, 1730.

DE MORGAN A.,
[1] Differential and Integral Calculus, Chapters XIII and XX, 1842.

DENCE J.B.,
[1] A development of Euler numbers, Missouri J. Math. Sci. 9 (1997), no. 3, 148-155.
M 98h:11023

DENCE J.B., DENCE Th. P.,
[1] Elements of the theory of numbers. Harcourt/Academic Press, San Diego, CA, 1999. xviii+517 pp. ISBN 0-12-209130-2
Z916.05001; M99k:11001

DÉNES P.,
[1] An extension of Legendre's criterion in connection with the first case of Fermat's last theorem, Publ. Math. Debrecen, 2 (1951), 115-120.
Z43.27302; M13-822h

[2] Über die Diophantische Gleichung $x^{np + y^{np} = p^mz^{np}$, Czechoslovak Math. J. 1, 76 (1951) (1952), 179-185.
Z48.02904; M16-903g

[3] Beweis einer Vandiver'schen Vermutung bezüglich des zweiten Falles des letzten Fermat'schen Satzes, Acta Sci. Math. (Szeged), 14 (1952), 197-202.
Z49.31003; M14-451e

[4] Über die Diophantische Gleichung $x^l+y^l = cz^l$, Acta Math., 88 (1952), 241-251.
Z48.27503; M16-903h

[5] Über irreguläre Kreiskörper, Publ. Math. Debrecen, 3 (1953) (1954), 17-23.
Z56.03301; M15-686d; R1955,3043

[6] Über Grundeinheitssysteme der irregulären Kreiskörper von besonderen Kongruenzeigenschaften, Publ. Math. Debrecen, 3 (1954) (1955), 195-204.
Z58.26902; M17-131c; R1957,69

[7] Über den zweiten Faktor der Klassenzahl und den Irregularitätsgrad der irregulären Kreiskörper, Publ. Math. Debrecen, 4 (1956), 163-170.
Z71.26505; M18-20e; R1959,4421

DENINGER CH.,
[1] On the analogue of the formula of Chowla and Selberg for real quadratic fields, J. Reine Angew. Math., 351 (1984), 171-191.
Z527.12009; M86f:11085; R1985,1A215

DENNLER G.,
[1] Bestimmung sämtlicher meromorpher Lösungen der Funktionalgleichung $f(z) = {1 \over k} \sum_{h=0}^{k-1}{f({z+h \over k})}$, Wiss. Z. Friedrich-Schiller-Univ. Jena, Math.-Natur., 14 (1965), no. 5, 347-350.
Z146.13202; M37#5559; R1968,1B202

DE PESLOUAN L.,
[1] Sur une congruence entre les nombres de Bernoulli, C. R. Acad. Sci. Paris, 170 (1920), 267-269.
J47.0131.04

DEPINE R.A.: see BANUELOS A., DEPINE R.A.

DERR L.: see OUTLAW C., SARAFYAN D., DERR L.

DERUYTS J.,
[1] Rapport sur un Mémoire de M. Beaupain intitulé: ``Sur une classe de fonctions qui se rattachent aux fonctions de Jacques Bernoulli.'' Belg. Bull. Sciences (1900), 255-257.
J31.0438.01

Désarménien, Jacques,
[1] Un analogue des congruences de Kummer pour les $q$-nombres d'Euler. European J. Combin. 3 (1982), no. 1, 19-28.
M83k:05007

DESBROW D.,
[1] Sums of integer powers, Math. Gaz., 66 (1982), no. 436, 97-100.
M83j:10054

DESNOUX P.-J.,
[1] Congruences dyadiques entre nombres de classes de corps quadratiques, Manuscr. Math., 62 (1988), no. 2, 163-179.
Z664.12002; M90c:11079; R1989,4A265

DE TEMPLE D. W., WANG SHUN HWA,
[1] Half-integer approximations for the partial sums of the harmonic series, J. Math. Anal. Appl., 160 (1991), no. 1, 149-158.
Z747.40002; M92j:41042

DEVANATHAN V.: see SUBRAMANIAN P.R., DEVANATHAN V.

DIAMOND F.: see DARMON H., DIAMOND F., TAYLOR R.,

DIAMOND J.,
[1] The $p$-adic log gamma function and $p$-adic Euler constants, Trans. Amer. Math. Soc. 233 (1977), 321-337.
Z382.12008; M58 #16610

[2] The p-adic gamma measures, Proc. Amer. Math. Soc., 75 (1979), no. 2, 211-218.
Z421.12019; M80d:12013; R1980,1A369

[3] On the values of p-adic L-functions at positive integers, Acta Arith., 35 (1979), no. 3, 223-237.
Z463.12007; M80j:12013; R1980,5A313

DIBAG I.,
[1] An analogue of the von Staudt-Clausen theorem, J. Algebra, 87 (1984), Suppl., no. 2, 332-341.
Z536.10012; M85j:11028; R1984,10A308

[2] Generalisation of the von Staudt-Clausen theorem, J. Algebra, 125 (1989), no. 2, 519-523.
Z683.10014; M90g:11025; R1990,5A275

DI CAVE A., RICCI P.E.,
[1] Sui polinomi di Bell ed i numeri di Fibonacci e di Bernoulli, Matematiche, 35 (1980), no. 1-2, 84-95.
Z534.33008; M84h:05011

DI BUCCHIANICO A., LOEB D.,
[1] A selected survey of umbral calculus. Electron. J. Combin. 2 (1995), Dynamic Survey 3, 28 pp. (electronic).
Z851.05012; M99j:05017

DI BUCCHIANICO A., LOEB D., ROTA G.-C.,
[1] Umbral calculus in Hilbert space. Mathematical essays in honor of Gian-Carlo Rota (Cambridge, MA, 1996), 213-238, Progr. Math., 161, Birkhäuser Boston, Boston, MA, 1998.
Z902.05007; M 99i:05021

DICKEY L.J., KAIRIES H.H., SHANK H.S.,
[1] Analogs of Bernoulli polynomials in fields $ Z_p$, Aequationes Math., 14 (1976), no. 3, 401-440.
Z343.12006; M53#13103; R1977,2A117

DICKSON J.D.H.,
[1] On Raabe's Bernoullians. Proc. London Math. Soc. 20 (1889), 14-21.
J21.0247.03

DICKSON J.D.H.: see also BARNIVILLE J.J., DICKSON J.D.H., LAMPE E.

DICKSON L.E.,
[1] Notes on the theory of numbers, Amer. Math. Monthly, 18 (1911), 109-111.

[2] History of the Theory of Numbers, Washington, (1919-1923), vol. 1-3. Reprint: Chelsea Publ. Co., New York, 1966.
J47.0100.04; J49.0100.12; J60.0817.03; M39#6807a,b,c

DI CRESCENZO A., ROTA G.-C.,
[1] On umbral calculus (Italian. English summary), Ricerche Mat., 43 (1994), no. 1, 129-162.
Z918.05010; M96e:05016

DIENGER J.,
[1] Die Lagrangesche Formel und die Reihensummierung durch dieselbe, J. Reine Angew. Math., 34 (1847), 75-100.

DIETER U.,
[1] Reciprocity theorems for Dedekind sums, IX. Mathematikertreffen Zagreb-Graz (Motovun, 1995), 11-24, Grazer Math. Ber., 328, Karl-Franzens-Univ. Graz, Graz, 1996.
Z880.11041; M98i:11024

DILCHER K.,
[1] Zero-free regions for Bernoulli polynomials, C.R. Math. Rep. Acad. Sci. Canada, 5 (1983), no. 6, 241-246.
Z532.30005; M85a:30015; R1984,3B30

[2] Irreducibility and zeros of generalized Bernoulli polynomials, C.R. Math. Rep. Acad. Sci. Canada, 6 (1984), no. 5, 273-278.
Z558.10012; M85k:11010; R1985,7A148

[3] On a Diophantine equation involving quadratic characters, Compositio Math., 57 (1986), no. 3, 383-403.
Z584.10008; M87e:11046; R1986,8A99

[4] Irreducibility of certain generalized Bernoulli polynomials belonging to quadratic residue class characters, J. Number Theory, 25 (1987), no. 1, 72-80.
M88a:11021; R1987,6A98

[5] Asymptotic behaviour of Bernoulli, Euler and generalized Bernoulli polynomials, J. Approx. Theory, 49 (1987), no. 4, 321-330.
Z609.10008; M88g:33001; R1987,10A63

[6] Zeros of Bernoulli, generalized Bernoulli and Euler polynomials, Mem. Amer. Math. Soc., 73 (1988), no. 386, iv + 94 pp.
Z645.10015; M89h:30005; R1988,10B22

[7] Multiplikationstheoreme f¨r die Bernoullischen Polynome und explizite Darstellungen der Bernoullischen Zahlen, Abh. Math. Sem. Univ. Hamburg, 59 (1989), 143-156.
Z712.11015; M91h:11012

[8] Sums of products of Bernoulli numbers. J. Number Theory, 60 (1996), no. 1, 23-41.
Z863.11011; M97h:11014

[9] Von Staudt-Clausen Theorem. Encyclopedia of Mathematics, Supplement II. Kluwer Academic Publishers, Dordrecht, 2000.

[10] Bernoulli numbers and confluent hypergeometric functions. Number theory for the millennium, I (Urbana, IL, 2000), 343-363, A K Peters, Natick, MA, 2002.
M2003m:11032

DILCHER K., MALLOCH L.,
[1] Arithmetic properties of Bernoulli-Padé numbers and polynomials. J. Number Theory 92 (2002), no. 2, 330-347.
M2003b:11013

DILCHER K., SKULA L.,
[1] A new criterion for the first case of Fermat's last theorem. Math. Comp. 64 (1995), no. 209, 363-392.
Z817.11022; M95c:11034

DILCHER K., SKULA L., SLAVUTSKII I. SH.,
[1] Bernoulli Numbers. Bibliography (1713-1990). Queen's Papers in Pure and Applied Mathematics, 87, Queen's University, Kingston, Ont., 1991.
Z741.11001; M92f:11001; R1992,4A54

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

DILCHER K.: see also AGOH T., DILCHER K., SKULA L.

DILCHER K.: see also CRANDALL R.E., DILCHER K., POMERANCE C.

DILLON J.F., ROSELLE D.P.,
[1] Eulerian numbers of higher order, Duke Math. J., 35 (1968), no. 2, 247-256.
Z185.03003; M37#1261; R1969,1V229

DI MARZIO F.,
[1] The very accurate summation of inverse powers and the generation of Bernoulli and Euler numbers, Comput. Phys. Comm., 44 (1987), no. 1-2, 57-62.
Z673.10008; M88f:65014; R1988,2B36

DINTZL E.,
[1] Über Zahlen im Körper $k({\sqrt{-2)$, welche den Bernoullischen Zahlen analog sind, Sitz. Akad. Wiss., Wien, Math. und natur. Kl., 2e Abteil., 118 (1909), 173-201.
J40.0265.02

[2] Über einige Eigenschaften der Bernoullischen und analoger Zahlen, Jb. k. k. Erzherzog-Rainer-Realgymnasium Wien, (1910), 1-11.
J41.0503.03

[3] Über die Entwicklungscoeffizienten der elliptischen Funktionen, insbesondere im Falle singulärer Moduln, Monatsh. Math. und Physik, 25 (1914), 125-151.
J45.0685.01

DITTRICH G.,
[1] Die Theorie des Fermat-Quotienten, Dissertation, Jena, 1924.

D'OCAGNE M.: see d'OCAGNE M.

DOKOVIC D.,
[1] Formule pour le calcul des puissances semblables des nombres naturels, (Serbo-Croatian, French summary), Bull. Soc. Math. Phys. Macédoine 8 (1957), 38-40.
M23#A97

DOKSHITZER T.,
[1] On Wilf's conjecture and generalizations. In: Number Teory (K. Dilcher, Ed.), Fourth Conference of the Canadian Number Theory Association (Halifax, July 2-8, 1994), CMS Conference Proceedings 15, 133-153. Amer. Math. Soc., Providence, 1995.
Z837.11023; M96h:11031

DOLZE P.,
[1] Über Bernoullische Zahlen und Funktionen, welche zu einer Fundamentaldiskriminante gehören, und deren Anwendung auf die Summation unendlicher Reihen. Inaugurationsdissertation, Rostock, 44p. Dresden, 1907.
J37.0300.02; J38.0466.02

Domaratzki, Michael,
[1] Combinatorial interpretations of a generalization of the Genocchi numbers. J. Integer Seq. 7 (2004), no. 3, Article 04.3.6, 11 pp. (electronic).
M2005h:11031

DONAGHEY R.,
[1] Binomial self-inverse sequences and tangent coefficients, J. Combin. Theory A, 21 (1976), no. 2, 155-163.
Z345.05002; M54#2475; R1977,3V372

DÖRFLER P.,
[1] A Markov type inequality for higher derivatives of polynomials, Monatsh. Math., 109 (1990), no. 2, 113-122.
Z713.41006; M91h:26017

DOWLING J.P.,
[1] The mathematics of the Casimir effect, Math. Magazine, 62 (1989), no. 5, 324-333.
M91a:81229

DOYON B., LEPOWSKY J., MILAS A.,
Twisted modules for vertex operator algebras and Bernoulli polynomials. Int. Math. Res. Not. 2003, no. 44, 2391-2408.
M2005b:17055

Doyon, B.; Lepowsky, J.; Milas, A.,
[1] Twisted vertex operators and Bernoulli polynomials. Commun. Contemp. Math. 8 (2006), no. 2, 247--307.

DRYANOV D., KOUNCHEV O.,
[1] Polyharmonically exact formula of Euler-Maclaurin, multivariate Bernoulli functions, and Poisson type formula, C. R. Acad. Sci. Paris Sér. I Math., 327 (1998), no. 5, 15-520.
Z908.65003; M99j:65003; R1999,12G29

[2] Multivariate Bernoulli functions and polyharmonically exact cubature formula of Euler-Maclaurin. Math. Nachr. 226 (2001), 65-83.
M2002c:41043

DUBE P.P.: see PANJA G.K., DUBE P.P.

DUCCI E.,
[1] Somma della potenze simili dei termini di una progressione per differenza, Giorn. Matem., Napoli, 23 (1894), 348-352.
J25.0411.01

DUKE W., IMAMOGLU Ö.,
[1] Siegel modular forms of small weight, Math. Ann. 310 (1998), no. 1, 73-82.
Z892.11017; M98m:11037

DUMAS P., FLAJOLET P.,
[1] Asymptotique des récurrences mahlériennes: le cas cyclotomique, J. Théor. Nombres Bordeaux 8 (1996), no. 1, 1-30.
Z869.11080; M97f:39029

DUMMIGAN N.,
[1] Period ratios of modular forms. Math. Ann. 318 (2000), no. 3, 621-636.
M2002a:11049

DUMONT D.,
[1] Sur une conjecture de Gandhi concernant les nombres de Genocchi, Discrete Math., 1 (1972), no. 4, 321-327.
Z263.10005; M45#5073; R1974,7B461

[2] Propriétés géométriques des nombres de Genocchi, Thèse, Strasbourg, 1973.

[3] Interprétations combinatoires des nombres de Genocchi, Duke Math. J., 41 (1974), 305-318.
Z297.05004; M49#2412; R1985,3V437

[4] Conjectures sur des symétries ternaires liées aux nombres de Genocchi, Discrete Math., 139 (1995), no. 1-3, 469-472.
Z823.05003; M96e:05007

[5] Further triangles of Seidel-Arnold type and continued fractions related to Euler and Springer numbers. Adv. in Appl. Math. 16 (1995), no. 3, 275-296.
Z834.05004; M96i:11021

DUMONT D., FOATA D.,
[1] Une propriété de symétrie des nombres de Genocchi, Bull. Soc. Math. France, 104 (1976), no. 4, 433-451.
Z362.05018; M55#7794

DUMONT D., RANDRIANARIVONY A.,
[1] Dérangements et nombres de Genocchi, Discrete Math., 132 (1994), no. 1-3, 37-49.
Z807.05001; M95h:05015

[2] Sur une extension des nombres de Genocchi, European J. Combin., 16 (1995), no. 2, 147-151.
Z823.05004; M96k:11015

DUMONT D., VIENNOT G.,
[1] A combinatorial interpretation of the Seidel generation of Genocchi numbers. Ann. Discrete Math., 6 (1980), 77-87.
Z449.10011; M82j:10024; R1981,8V588

DUMONT D., ZENG J.,
[1] Further results on the Euler and Genocchi numbers. Aequationes Math., 47 (1994), no. 1, 31-42.
Z805.11024; M95b:11021

[2] Polynômes d'Euler et fractions continues de Stieltjes-Rogers, Ramanujan J. 2 (1998), no. 3, 387-410.
M99i:05008

DUMONT D.: see also BARSKY D., DUMONT D.

DUPARC H.J.A., PEREMANS W.,
[1] On certain representations of positive integers, Nieuw. Arch. Wisk. (3), 1 (1953), no. 2, 92-98.
Z50.26905; M15-288e; R1954,2853

DUPUIS N.F.,
[1] Cruces mathematicae [Sect. 4: Expression of the general Bernoullian number as a combinational determinant]. Royal Society of Canada, Proc. and Trans. 7 (1889), Sect. 3, 15-22.

DUTKA J.,
[1] On the summation of some divergent series of Euler and the zeta functions. Arch. Hist. Exact Sci. 50 (1996), no. 2, 187-200.
Z858.01018; M98a:11112; R1997,5A6


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