Bernoulli Bibliography

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WAALL R.W. van der,
[1] On a property of $\tan x$, J. Number Theory, 5 (1973), 242-244.
Z266.10014; M48#8375

WADA H.,
[1] Some computations on the criteria of Kummer, Tokyo J. Math., 3 (1980), no. 1, 173-176.
Z448.10016; M81m:10028; R1981,2A128

WAGON S.,
[1] Fermat's last theorem, Math. Intelligencer, 8 (1986), no. 1, 59-61.
M87e:11045; R1986,8A102

WAGSTAFF S.S. JR.,
[1] Zeros of p-adic L-functions, Math. Comp., 29 (1975), no. 132, 1138-1143.
Z315.12009; M52#8096; R1976,9A369

[2] The irregular primes to 125000, Math. Comp., 32 (1978), no. 142, 583-591.
Z377.12002; M58#10711; R1979,1A164

[3] Proof of a formula of Ramanujan concerning Bernoulli numbers, Notices Amer. Math. Soc., 26 (1979), A-330.

[4] p-divisibility of certain sets of Bernoulli numbers, Math. Comp., 34 (1980), no. 150, 647-649.
Z424.10013; M81i:10018; R1980,11A67

[5] Zeros of p-adic L-functions, 2, Number Theory Related to Fermat's Last Theorem (N. Koblitz, ed.), Progress in Math., No. 26, Birkhäuser, Boston, Mass., 1982, 297-308.
Z498.12015; M84h:12027; R1985,4A335

[6] Ramanujan's paper on Bernoulli numbers, J. Indian Math. Soc. N.S.(9), 45 (1981), no. 1-4, 49-65 (1984).
Z636.10010; M87h:11019; R1956,8V689

[7] Prime divisors of the Bernoulli and Euler numbers. Number theory for the millennium, III (Urbana, IL, 2000), 357-374, A K Peters, Natick, MA, 2002.
M2003m:11039

WAGSTAFF S.S., JR., TANNER J.W.,
[1] New congruences for the Bernoulli numbers, Math. Comp., 48 (1987), no. 177, 341-350.
Z613.10012; M87m:11017

WAGSTAFF S.S. JR.: see also ERDÖS P., WAGSTAFF S.S.

WAGSTAFF S.S. JR.: see also TANNER J.W., WAGSTAFF S.S.

WAHLIN G.E.: see VANDIVER H.S., WAHLIN G.E.

WAKAYAMA M.: see KANEKO M., KUROKAWA N., WAKAYAMA M.

WALDSCHMIDT M., MOUSSA P., LUCK J.-M., ITZYKSON C. (Eds.),
[1] From Number Theory to Physics. Springer-Verlag, Berlin etc., 1992, xiv+690 pp.
Z790.11061; M93m:11001

WALSH P.G.: see JACOBSON M.J., Jr., PINTÉR, Á., WALSH P.G.

WALSTRA, K.W.,
[1] Sur les fonctions de Lubbock. Nieuw Arch. Wisk. (2) 12 (1917), 161-168
J46.0359.02

WALTON W.,
[1] On certain transformations in the calculus of operations, Quart. J. Pure Appl. Math., 8 (1867), 222-227.

WALUM H.,
[1] Multiplication formulae for periodic functions, Pacific J. Math., 149 (1991), no. 2, 383-396.
Z736.11012; M92c:11019

van WAMELEN P.: see SCHINZEL A., URBANOWICZ J., VAN WAMELEN P.

WANG CHUNG LIE, WANG XING HUA,
[1] Refinements of the Mathieu inequality. (Chinese. English summary). J. Math. Res. Exposition, 1 (1981), no. 1, 107-112.
Z476.26008; M83j:26017; R1982,4B3

WANG GUAN MIN,
[1] An identity for proper Dirichlet series and Euler numbers (Chinese. English and Chinese summaries). Zhangzhou Shiyuan Xuebao (Ziran Kexue Ban), 8 (1994), no. 4, 85-8 8.

[2] Rao-Davis identities related to the Riemann zeta-function. (Chinese. English, Chinese summary). Zhangzhou Shiyuan Xuebao (Ziran Kexue Ban) 10 (1996), no. 2, 28-41, 47.
M97g:11091

Wang, Hai Lin; Luo, Jian Jin,
[1] Research on the relations between Euler numbers, Dai Xu numbers and gear mutation. (Chinese) Stud. Hist. Nat. Sci. 24 (2005), no. 1, 53-59.
M2006e:11026

WANG KAI,
[1] A proof of an identity of the Dirichlet L-functions, Bull. Inst. Math., Acad. Sin., 10 (1982), no. 3, 317-321.
Z497.10031; M84c:10040

[2] Exponential sums of Lerch's zeta functions, Proc. Amer. Math. Soc., 9 (1985), no. 1, 11-15.
Z573.10011; M86j:11084; R1986,6A189

[3] A proof of an identity of the Dirichlet L-function at negative integers, Bull. Inst. Math., Acad. Sin., 13 (1985), no. 2, 143-147.
Z591.10032; M87a:11078

Wang, Nian Liang,
[1] Sum of products involving Bernoulli polynomials and Euler polynomials. (Chinese) Basic Sci. J. Text. Univ. 17 (2004), no. 4, 292-295.

WANG SHUN HWA: see DE TEMPLE D.W., WANG SHUN HWA

WANG TIAN MING, ZHANG XIANG DE,
[1] Some identities related to Genocchi numbers and the Riemann zeta-function, J. Math. Res. Exposition, 17 (1997), no. 4, 597-600.
Z902.11011; R1996,11V258

WANG TIANMING, ZHANG ZHIZHENG,
[1] Recurrence sequences and Nörlund-Euler polynomials, Fibonacci Quart., 34 (1996), no. 4, 314-319.
Z861.11011; M97c:11024

WANG XING HUA: see WANG CHUNG LIE, WANG XING HUA

WANG YUN KUI,
[1] General expressions for sums of equal powers and Bernoulli numbers. (Chinese. English, Chinese summary) J. Guangxi Univ. Nat. Sci. Ed. 24 (1999), no. 4, 318-320.
M2001b:11017

WANG YUN KUI, MA WU YU
[1] Necessary and sufficient conditions for Bernoulli's numbers and discriminant prime numbers. (Chinese) J. Huaqiao Univ. Nat. Sci. Ed. 21 (2000), no. 3, 234-238.
M2001f:11034

WANG Z.X., GUO D.R.,
[1] Special functions. World Scientific, Singapore, etc., 1989, xviii+695pp.
Z724.33001; M91a:33001

WASHINGTON L.C.,
[1] A note on p-adic L-functions, J. Number Theory, 8 (1976), no. 2, 245-250.
Z329.12017; M53#10766; R1977,2A410

[2] The calculation of $L_p(1,chi)$, J. Number Theory, 9 (1977), no. 2, 175-178.
Z363.12019; M55#12704; R1977,11A145

[3] The non-p-part of the class number in a cyclotomic $ Z_p$-extension, Invent. Math., 49 (1978), no. 1, 87-97.
Z403.12007; M80c:12005; R1979,4A397

[4] Euler factors for p-adic L-functions, Mathematika, 25 (1978), no. 1, 68-75.
M58#22025

[5] Kummer's calculation of $L_p(1,{\chi})$, J. Reine Angew. Math., 305(1979), 1-8.
Z398.12019; M80e:12017; R1979,8A80

[6] Units of irregular cyclotomic fields, Illinois J. Math., 23 (1979), no. 4, 635-647.
Z423.12005; Z423.12005;427.12004; M81a:12006; R1980,7A312

[7] Zeros of p-adic L-functions, Sém. théor. nombres, 1980-81, Univ. Bordeaux I, Talence, 1981, Exp. No. 25, 4 pp.
Z479.12005; M82m:10006; R1985,4A334

[8] p-adic L-functions at $s=0$ and $s=1$, Analytic number theory, Lect. Notes in Math., 899 (1981), 166-170.
Z479.12004; M83m:12019

[9] The derivative of p-adic L-functions, Acta. Arith., 40 (1981), no. 1, 109-115.
Z483.12001; M83m:12020; R1982,10A298

[10] Introduction to cyclotomic fields, New York, Springer-Verlag, 1982.
Z484.12001; M85g:11001; R1982,12A356K; Z484.12001; M85g:11001; R1982,12A356K;1983,4A368K

[11] Recent results on cyclotomic fields, Algebraic Topology, 1981, Sem. notes, Inst. of Math., Univ. of Aarhus, 1982, No. 1, 120-129.
Z502.12003; M83k:12003; R1983,7A154

[12] Zeroes of p-adic L-functions, Progress in Math., Boston, No. 22, (1982), 337-357 (Théor. des Nombres. Paris, 1980-81, Sémin. Delange-Pisot-Poitou).
Z495.12015; M84f:12008; R1985,4A334

[13] On some cyclotomic congruences of F. Thaine, Proc. Amer. Math. Soc., 93 (1985), no. 1, 10-14.
Z564.10010; M86c:11019; R1986,2A331

[14] On Sinnott's proof of the vanishing of the Iwasawa invariant $\mu_p$. Algebraic number theory, 457-462, Adv. Stud. Pure Math., 17, Academic Press, Boston, MA, 1989.
Z732.11059; M92e:11123

[15] Introduction to cyclotomic fields. Second edition. Graduate Texts in Mathematics, 83. Springer-Verlag, New York, 1997. xiv+487 pp.
Z0966.11047; M97h:11130

[16] $p$-adic $L$-functions and sums of powers, J. Number Theory, 69 (1998), no. 1, 50-61.
Z910.11047; M99a:11134

WASHINGTON L.C.: see also ADLER A., WASHINGTON L.C.

WASHINGTON L.C.: see also FERRERO B., WASHINGTON L.C.

WASHINGTON L.C.: see also FRIEDMAN E., SANDS J. W.

WATSON G.N.,
[1] Theorems stated by Ramanujan (II): Theorems on summation of series, J. London Math. Soc., 3 (1928), 216-225.
J54.0229.04

WATSON G.N.: see also ADIGA C., BERNDT B.C. et al.

WATSON G.N.: see also WHITTAKER E.T., WATSON G.N.

WEIHRAUCH K.,
[1] Untersuchungen über eine Gleichung des ersten Grades mit mehreren Unbekannten, Diss. Dorpat, 1869.
J02.0051.03

[2] Die Anzahl der Lösungen diophantischer Gleichungen bei theilfremden Coefficienten, Zeitsch. für Math., 20 (1875), 97-111.
J07.0093.01

[3] Über die Ausdrücke $\sum f_n(m)$ und die Umgestaltungen der Formel für die Lösungsanzahlen Anwendung der Formel in der Combinationslehre, Zeitsch. für Math., 20 (1875), 112-117.
J07.0093.02

[4] Anzahl der Auflösungen einer unbestimmten Gleichung für einen speciellen Fall von nicht theilfremden Coefficienten, Zeitsch. für Math., 20 (1875), 314-316.
J07.0093.03

[5] Anzahl der Lösungen für die allgemeinste Gleichung ersten Grades mit vier Unbekannten, Zeitsch. für Math., 22 (1877), 234-244.
J09.0134.01

[6] Theorie der Restreihen zweiter Ordnung, Zeitsch. für Math., 32 (1887), 1-21.
J19.0179.02

WEIL A.,
[1] L'oeuvre arithmétique d'Euler. "Leonhard Euler. 1707-1783: Beiträge zu Leben und Werk", Birkhäuser, Basel, 1983, 111-134.
Z516.01012; M84m:01021; R1984,7A13

[2] Number Theory. An Approach Through History From Hammurapi to Legendre. Birkhäuser, Boston etc., 1984, xxi + 375pp.
Z531.10001; M85c:01004

WEINMANN A.,
[1] Asymptotic expansions of generalized Bernoulli polynomials, Proc. Camb. Phil. Soc., 59 (1963), no. 1, 73-80.
Z114.03407; M29#5009; R1963,10B66

WEISS A.: see RITTER J., WEISS A.

WESTLUND J.,
[1] On the class number of the cyclotomic number field $k(e{{2 \pi i}\over{p^n})$, Trans. Amer. Math. Soc., 4 (1903), 201-212.
J34.0237.02

WHITTAKER E.T., WATSON G.N.,
[1] A Course of Modern Analysis, 4th Edition. Cambridge University Press, Cambridge, 1927.
J53.0180.04

WICKE F.,
[1] Über ultra-Bernoullische und ultra-Eulersche Zahlen und Funktionen und deren Anwendung auf die Summation von Reihen, Diss. Jena, 1905, 68 p.
J36.0498.02

WIEFERICH A.,
[1] Zum letzten Fermatschen Theorem, J. Reine Angew. Math., 136 (1909), no. 4, 293-302.
J40.0256.03

WILES A.,
[1] Modular curves and the class group of $Q(\zeta_p)$, Invent. Math., 58 (1980), no. 1, 1-35.
Z436.12004; M82j:12009; R1980,10A274

WILES A.: see also MAZUR B., WILES A.

WILES A.: see also RUBIN K., WILES A.

WILKINSON K.M.: see RUDOLFER S.M., WILKINSON K.M.

WILLIAMS G.T.,
[1] A new method of evaluating ${\zeta}(2n)$, Amer. Math. Monthly, 60 (1953), no. 1, 19-25.
Z50.06803; M14,536j; R1953,31

WILLIAMS H.: see BEACH B., WILLIAMS H., ZARNKE C.

WILLIAMS H.C.: see FUNG G., GRANVILLE A., WILLIAMS H.C.

WILLIAMS H.C.: see STEPHENS A.J., WILLIAMS H.C.

WILLIAMS H.C.: see van der POORTEN A.J., te RIELE, H.J.J., WILLIAMS H.C.

WILLIAMS K.P.,
[1] Relating to some determinants connected with the Bernoulli numbers, Amer. Math. Monthly, 23 (1916), 263-266.

WILLIAMS K.S.,
[1] On $\sum_{n=1}^\infty (1/n^{2k})$, Math. Mag., 44 (1971), no. 5, 273-276.
Z224.40008; M45#3997; R1972,6B17

[2] Bernoulli's identity without calculus. Math. Mag. 70 (1997), no. 1, 47-50.
Z880.11023; M98c:05015

WILLIAMS K.S., ZHANG NAN-YUE,
[1] Special values of the Lerch zeta-function and the evaluation of certain integrals. Proc. Amer. Math. Soc., 119 (1993), no. 1, 35-49.
Z785.11046; M93k:11081

[2] Evaluation of two trigonometric sums, Math. Slovaca, 44 (1994), no. 5, 575-583.
Z820.11010; M96d:11088

[3] Values of the Riemann zeta function and integrals involving $\log(2\,{\rm sinh}(\theta/2))$ and $\log(2\sin(\theta/2))$, Pacific J. Math. 168 (1995), no. 2, 271-289.
Z828.11041; M96f:11170

WILLIAMS K.S.: see also FOX G.J., URBANOWICZ J., WILLIAMS K.S.

WILLIAMS K.S.: see also URBANOWICZ J., WILLIAMS K.S.

WILLIOT V.,
[1] Note sur le procédé le plus simple de calcul des nombres de Bernoulli, Bull. Soc. Math. France, 16 (1888), 144-149.
J20.0265.01

WILSON B.M.: see BERNDT B.C. et al.

WILSON J.C.,
[1] On Franel-Kluyver integrals of order three, Acta Arith., 66 (1994), no. 1, 71-87.
Z807.11013; M94m:11116; R1997,12A60

WILSON J.C.: see also HALL R.R. et al.

WILTON J.R.,
[1] A proof of Burnside's formula for $log {\Gamma}(x+1)$ and certain allied properties of Riemann's $\zeta$-function, Messeng. Math. (2), 52 (1923), 90-93.
J48.0409.04

WIRTINGER W.,
[1] Einige Anwendungen der Euler-Maclaurinschen Summenformel, insbesondere auf eine Aufgabe von Abel. Acta Math. 26 (1902), 255-272.
J33.0454.01

WOLFF H.,
[1] Über die Anzahl der Zerlegungen einer ganzen Zahl in Summen, Diss. Halle, 1899.
J30.0201.09

WONG E.: see also BORWEIN J.M., WONG E.

WONG R., ZHANG J.-M.,
[1] Asymptotic monotonicity of the relative extrema of Jacobi polynomials, Canad. J. Math., 46 (1994), no. 6, 1318-1337.
Z819.33004; M95j:33029

WOODCOCK C.F.,
[1] An invariant p-adic integral on $ Z_p$, J. London Math. Soc., (2), 8 (1974), 731-734.
Z292.12021; M50#4545; R1975,6A461

[2] A note on some congruences for the Bernoulli numbers $B_m$, J. London Math. Soc. (2), 11 (1975), no. 2, 256.
Z335.10017; M56#5415; R1976,3A162

[3] A two variable Riemann zeta function, J. Number Theory, 27 (1987), no. 2, 212-221.
Z623.10028; M88k:11057; R1988,3B32

[4] Special $p$-adic analytic functions and Fourier transforms. J. Number Theory 60 (1996), no. 2, 393-408.
Z0860.11071; M98a:11169

WOOLRIDGE K.,
[1] Some results in Arithmetical Functions Similar to Euler's Phi-Function, Ph.D. thesis, Univ. of Illinois, 1975. Ch. III: Numerical Data on Irregular Primes, 32-41.

WOON S.C.,
[1] A tree for generating Bernoulli numbers, Math. Mag. 70 (1997), no. 1, 51-56.
Z882.11014; M98a:11026

WORONTZOF M.M. (WORONTZOFF M.),
[1] On the generalization of certain formulae investigated by Mr. Blissard, Quart. J. Math., 8 (1867), 185-208, 310-319.

[2] Sur les nombres de Bernoulli, Nouv. Ann. Math. (2), 15 (1876), 12-19.
J08.0146.01

WORPITZKY J.,
[1] Studien über die Bernoullischen und Eulerschen Zahlen, J. Reine Angew. Math., 94 (1883), 203-232.
J15.0201.01

[2] Über die Partialbruchzerlegung der Functionen, mit besonderer Anwendung auf die Bernoulli'schen, Zeit. für Math. und Phys., 29 (1884), 45-54.
J16.0394.02

WRIGGE S.,
[1] Calculation of the Taylor series expansion coefficients of the Jacobian elliptic unction sn(x,k), Math. Comp. 37 (1981), no. 156, 495-497.
Z479.33003; M82d:65023

[2] An analytic disproof of Robertson's conjecture, J. Math. Anal. Appl., 154 (1991), no. 1, 80-82.
Z739.30002; M92a:05012

WRIGHT E.M.: see HARDY G.H., WRIGHT E.M.

Wu, Ke-Jian; Sun, Zhi-Wei; Pan, Hao,
[1] Some identities for Bernoulli and Euler polynomials. Fibonacci Quart. 42 (2004), no. 4, 295-299.
Z1064.11019; M2006a:11024

WU YUN FEI,
[1] A computational formula for a class of identities involving Bernoulli polynomials, Math. Practice Theory, 1995, no. 2, 32-36.
M96j:11022; R1996,2A102


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