Bernoulli Bibliography

S

SAALSCHÜTZ L.,
[1] Zwei Abhandlungen aus dem Gebiete der Bernoullischen Zahlen, Schrift. Phys.-ökonom. Gesell. Königsb. 33 (1892), 44-49.

[2] Verkürzte Recursionsformeln für die Bernoulli'schen Zahlen, Zeit. für Math. und Phys., 37 (1892), 374-378.
J24.0237.01

[3] Vorlesungen über die Bernoullischen Zahlen, ihren Zusammenhang mit den Secanten-Coefficienten und ihre wichtigeren Anwendungen, Springer-Verlag, Berlin, 1893. viii + 208 S.
J24.0236.01

[4] Studien zu Raabe's Monographie über die Jacob Bernoullische Funktion, Zeit. für Math. und Phys., 42 (1897), 1-13.
J28.0375.02

[5] Über Beziehungen zwischen den Anfangsgliedern von Differenzreihen und von deren Verwendung zu Summationen und zur Darstellung der Bernoullischen Zahlen, Schrift. Phys.-ökonom. Gesell. Königsb., 41 (1900), 14-17.

[6] Gleichungen zwischen den Anfangsgliedern von Differenzreihen und deren Verwendung zu Summationen und zur Darstellung der Bernoullischen Zahlen, J. Reine Angew. Math., 123 (1901), 210-240.
J32.0280.03

[7] Die ganzen Potenzen der Cotangente und der Cosecante nebst neuen Formeln für die Bernoullischen Zahlen. Schriften der physik-ökonom. Ges. zu Königsberg i. Pr., 44 (1903), 32p.
J34.0482.01

[8] Neue Formeln für die Bernoullischen Zahlen. J. Reine Angew. Math., 126 (1903), 99-101.
J34.0482.02

SACHKOV V.N.,
[1] Combinatorical methods of discrete mathematics. (Russian) Moscow: Nauka, 1977, 319 pp.
R1978,4V321

[2] Probabilistic methods in combinatorical analysis. (Russian) Moscow: Nauka, 1978, 287 pp.
Z517.05011; M80g:05002; R1979,2V7

[3] Introduction to combinatorical methods of discrete mathematics. (Russian) Moscow: Nauka, 1982, 384 pp.
M85g:05001

SACHSE A.,
[1] Ueber die Darstellung der Bernoullischen und Eulerschen Zahlen durch Determinanten, Arch. für Math. und Phys., 68 (1882), 427-432.
J14.0110.01; J14.0191.04

SAGAN B.E., ZHANG PING,
[1] Arithmetic properties of generalized Euler numbers, Southeast Asian Bull. Math. 21 (1997), no. 1, 73-78.
Z970.56656; M98h:11025

SAITO H.: see IBUKIYAMA T., SAITO H.

SAITO T.: see KATO K., KUROKAWA N., SAITO T.

SALIÉ H.,
[1] Eulersche Zahlen, Sammelband zu Ehren des 250. Geburtstags Leonhard Eulers, Akademie-Verlag, Berlin, 1959, 293-310.
Z106.03106; M24#A75; R1960,7814

[2] Arithmetische Eigenschaften der Koeffizienten einer speziellen Hurwitzschen Potenzreihe, Wiss. Z. Karl-Marx-Univ. Leipzig, Math.-Naturw. R., 12 (1963), 617-618.
Z117.27703; M29#58

[3] Über die Koeffizienten Blasiusscher Reihen, Math. Nachr., 14 (1955), 241-248.
M18,379i; R1957,3757

SAMI Z.,
[1] On the first case of Fermat's last theorem, Glas. Mat. Ser. III, 21(41) (1986), no.2, 259-269.
Z621.10012; M88g:11012; R1987,12A82

[2] A sequence of numbers $a^m_{j,n}$, Glas. Mat. Ser. III, 23(43) (1988), no. 1, 3-13.
Z657.10009; M90f:11014; R1989,4B463

[3] On a sequence of polynomials, Proceedings of the Mathematical Conference in Pristina 1994, 39-46, Univ. Pristina, Pristina, 1995.
Z885.11022; M98h:11028

[4] Sequence $a\sp m\sb {j,n}$ and Bernoulli numbers. Proceedings of the Mathematical Conference in Pristina 1994, 47-50, Univ. Pristina, Pristina, 1995.
Z885.11019; M98h:11029

SÁNCHEZ-PEREGRINO R.,
[1] The Lucas congruence for Stirling numbers of the second kind. Acta Arith. 94 (2000), no. 1, 41-52.
Z947.11012; M2001b:11018

[2] Closed formula for poly-Bernoulli numbers. Fibonacci Quart. 40 (2002), no. 4, 362-364.
Z1030.11006; M2003e:11022

[3] A note on a closed formula for Poly-Bernoulli numbers. Amer. Math. Monthly 109 (2002), no. 8, 755-756.

SANDHAM H.F.,
[1] Some infinite series, Proc. Amer. Math. Soc., 5 (1954), no. 3, 430-436.
M15-950f; R1955,3271

SÁNDOR J.,
[1] Remarks on Bernoulli polynomials and numbers, Stud. Cerc. Math., 41 (1989), no. 1, 47-49.
Z671.10009; M90h:11017

[2] On the open problems OQ.487 and OQ.507, Octogon Math. Mag. 9 (2001), no.1, 550-551; 558-559.
R01.07-13A84

SANDS J. W.: see FRIEDMAN E., SANDS J. W.

SANKARANARAYANAN A.,
[1] An identity involving Riemann zeta function. Indian J. Pure Appl. Math., 18 (1987), no. 9, 794-800.
Z625.10031; M88i:11059; R1988,3A156

SANKARANARAYANAN A.: see RAMACHANDRA K., SANKARANARAYANAN A.

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

SASVÁRI Z.,
[1] An elementary proof of Binet's formula for the gamma function, Amer. Math. Monthly 106 (1999), no. 2, 156-158.

SATGÉ Ph.: see RIBET K. [3].

SATO K.: see SHIRAI S., SATO K.

SATO M.,
[1] On formal fractions associated with the symmetric groups, J. Combin. Theory, Ser. A, 20 (1976), no. 1, 124-131.
Z335.10016; M52#13413; R1976,7V378

SATOH J.,
[1] $q$-analogue of Riemann's $\zeta$-function and $q$-Euler numbers, J. Number Theory, 31 (1989), no. 3, 346-362.
Z675.12010; M90d:11132

[2] The Iwasawa $\lambda\sb p$-invariants of $\Gamma$-transforms of the generating functions of the Bernoulli numbers, Japan. J. Math. (N.S.) 17 (1991), no. 1, 165--174.
Z739.11047; M92e:11122

[3] A construction of $q$-analogue of Dedekind sums. Nagoya Math. J., 127 (1992), 129-143.
Z761.11023; M93h:11022; R1976/77,5B12

[4] Construction of $q$-analogue by using Stirling numbers. Japan J. Math. (N.S.), 20 (1994), no. 1, 73-91.
Z808.11018; M95j:11015

[5] Sums of products of two $q$-Bernoulli numbers, J. Number Theory, 74 (1999), 173-180
Z916.11014; M99m:11019

[6] A recurrence formula for $q$-Bernoulli numbers attached to formal group. Nagoya Math. J. 157 (2000), 93-101.
M2001c:11025

[7] Another look at the $q$-analogue from the viewpoint of formal groups. Proceedings of the Jangjeon Mathematical Society, 145-159, Proc. Jangjeon Math. Soc., 1, Jangjeon Math. Soc., Hapcheon, 2000.
M2001k:11029

SAUZET O.,
[1] Théorie d'Iwasawa des corps $p$-rationnels et $p$-birationnels, Manuscripta Math. 96 (1998), no. 3, 263-273.
Z905.11047; M99h:11123

SAVEL'EV L.Ya.,
[1] Combinatorics and probability. (Russian) Novosibirsk: Nauka, 1975, 423 pp.
Z447.05001; M52#13395; R1975,9V3K

SAYER F.P.,
[1] The sums of certain series containing hyperbolic functions. Fibonacci Quart., 14 (1976), no. 3, 215-223.
Z344.40002; M54#5663; R1976/77,5B12

SCAROWSKY M.,
[1] On a formal analogue of the Bernoulli numbers, J. Number Theory, 19 (1984), no. 2, 228-232.
Z546.10021; M86h:11019; R1985,8A110

SCHÄFFER J.J.,
[1] The equation $1^p+ 2^p+ 3^p+ \cdots +n^p = m^q$, Acta Math., 95 (1956), no. 3-4, 155-189.
Z71.03702; M17-1187a; R1957,2878

SCHAPPACHER N., SCHOLL A.J.,
[1] The boundary of the Eisenstein symbol. Math. Ann., 290 (1991), no. 2, 303-321. Erratum: Math. Ann., 290 (1991), no. 4, 815.
Z729.11027; M93c:11037a/b

SCHARLAU W., OPOLKA H.,
[1] Von Fermat bis Minkowski. Eine Vorlesung über Zahlentheorie und ihre Entwicklung, Springer-Verlag, Berlin-New York, 1980. xi + 224pp.
Z426.10001; M82g:10001; R1981,3A85K

[2] From Fermat to Minkowski. Lectures on the theory of numbers and its historical development. (Translation of [1]). Springer-Verlag, New York- Berlin, 1985, xi + 184 pp.
Z551.10001; M85m:11003; R1985,8A102K

SCHEIBNER W.,
[1] Zur Theorie der Maclaurinschen Summenformel, Berichte über die Verhandlungen der Königl. Sächsischen Gesellschaft der Wissenschaften zu Leipzig, 9 (1857), 190-198.

SCHENDEL L.,
[1] Die Bernoullischen Funktionen und das Taylorsche Theorem nebst einem Beitrag zur analytischen Geometrie der Ebene in trilinearen Coordinaten, H. Costenoble, Jena, 1876.
J08.0133.02

[2] Zur Theorie der Reihen, Zeit. für Math. und Phys., 16 (1871), 211-227.
J03.0105.02

SCHERK H.F.,
[1] Über einen allgemeinen, die Bernoullischen Zahlen und die Coëfficienten der Secantenreihe zugleich darstellenden Ausdruck, J. Reine Angew. Math., 4 (1829), 299-304.

[2] Von den numerischen Coefficienten der Secantenreihe, ihrem Zusammenhange, und ihrer Analogie mit den Bernoullischen Zahlen. Gesammelte Mathematische Abhandlungen, Reimer, Berlin, 1825, 1-30.

SCHIKHOF W.H.,
[1] Ultrametric calculus. An introduction to $p$-adic analysis. Cambridge University Press, Cambridge-New York, 1984. viii+306 pp.
Z553.26006; M86j:11104

SCHIKORE K.,
[1] Die Bernoullischen Zahlen. Published by the author, Breslau, 1929. 1 p.
J55.0802.04

SCHINZEL A.,
[1] Sur les nombres composés $n$ qui divisent $a^n - a$, Rend. Circ. Mat. Palermo (2), 7 (1958), no. 1, 37-41.
Z83.26103; M21#4935; R1959,9761

SCHINZEL A., URBANOWICZ J., VAN WAMELEN P.,
[1] Class numbers and short sums of Kronecker symbols, J. Number Theory 78 (1999), no. 1, 62-84.
Z0934.11053; M2000g:11103

SCHLÄFLI L.,
[1] On Staudt's theorem relating to the Bernoullian numbers, Quart. J. Math., 6 (1864), 75-77.

SCHLÖMILCH O.,
[1] Ueber Bernoullische Zahlen und die Coefficienten der Secantreihen, Arch. für Math. und Phys., 1 (1841), 360-363.

[2] Ueber die recurrirende Bestimmung der Bernoullischen Zahlen, Arch. für Math. und Phys., 3 (1843), 9-18.

[3] Développement d'une formule qui donne en mème temps les nombres de Bernoulli et les coëfficients de la série qui exprime la sécante, J. Reine Angew. Math., 32 (1846), 360-364.

[4] Relationen zwischen den Facultätencoefficienten, Arch. für Math. und Phys., 9 (1847), 333-335.

[5] Uebungsaufgaben für Schüler. Arch. für Math. und Phys., 10 (1847), 340-341.

[6] Über die Summe der Reihe $1^m + \cdots + z^m$, Arch. für Math. und Phys., 10 (1847), 342-344.

[7] Theorie der Differenzen und Summen. Druck und Verlag von H.W. Schmidt, Halle, 1848, 241 pp.

[8] Neue Methode zur Summirung endlicher und unendlicher Reihen, Arch. für Math. und Phys., 12 (1849), 130-166.

[9] Übungsaufgaben für Schüler. III. Arithmetisches Theorem. Arch. für Math. und Phys., 14 (1850), 108-109.

[10] Neue Formeln zur independenten Bestimmung der Sekanten- und Tangentenkoeffizienten, Arch. für Math. und Phys., 16 (1851), 411-418.

[11] Handbuch der algebraischen Analysis, 2te Auflage. Druck und Verlag von Fr. Frommann, Jena, 1851. viii + 344 pp.

[12] Über die independente Bestimmung der Coëfficienten unendlicher Reihen und der Facultätencoefficienten insbesondere, Arch. für Math. und Phys., 18 (1852), 306-327.

[13] Über die Bernoulli'schen Funktion und deren Gebrauch bei der Entwickelung halbconvergenter Reihen, Zeit. für Math. und Phys. (2), 1 (1856), 193-211.

[14] Über ein allgemeines Princip für Reihenentwickelungen, Zeitsch. für Math. und Phys., 2 (1857), 289-298.

[15] Über die Lambert'sche Reihe, Zeit. für Math. und Phys. (2), 6 (1861), 407-415.

[16] Compendium der höheren Analysis. Band 2. Braunschweig, 1862.

[17] Die Bernoulli'schen Funktionen und die halbconvergenten Reihen, Compendium der höheren Analysis, II (1874), 207-238.

SCHMIDT C.-G.,
[1] The p-adic L-functions attached to Rankin convolutions of modular forms, J. Reine Angew. Math., 368 (1986), 201-220.
Z585.10020; M88e:11038; R1986,12A586

SCHMIDT C.-G.: see also BÖCHERER S., SCHMIDT C.-G.,

SCHMIDT H.,
[1] Asymptotische Entwicklung von verallgemeinerten Bernoullischen Funktionen und von Teilsummen Dirichletscher Reihen mit periodischer Koeffizientenfolge, Collection of articles dedicated to Helmut Hasse on his seventy-fifth birthday, III, J. Reine Angew. Math., 274/275 (1975), 94-103.
Z312.10027; M52#303; R1975,12A143

[2] Zur Theorie und Anwendung Bernoulli-Nörlundscher Polynome und gewisser Verallgemeinerungen der Bernoullischen und der Stirlingschen Zahlen, Arch. Math. (Basel), 33 (1979), no. 4, 364-374.
Z438.10011; M81i:10017; R1980,11V460

SCHMIDT M.: see BUTZER P.L. et al.

SCHMIDT P.,
[1] The Stickelberger element of an imaginary quadratic field, Acta Math. 91 (1999), no. 2, 165-169.

SCHMIT C.: see BALAZS N.L., SCHMIT C., VOROS A.

SCHMITZ E.,
[1] Asymptotic expansions for the coefficients of $e^{P(z)}$, Bull. London Math. Soc., 21 (1989), 482-486.

SCHNEIDER I.,
[1] Potenzsummenformeln im 17. Jahrhundert. Historia Math. 10 (1983), no. 3, 286-296.
Z0522.01004; M85h:01017

SCHNEIDER P.,
[1] Über die Werte der Riemannschen Zeta-funktion an den ganzzahligen Stellen, J. Reine Angew. Math., 313 (1980), 189-194.
Z422.10030; M82g:10057; R1980,8A120

SCHOENBERG I.J.,
[1] Monosplines and quadrature formulae. 1969 Theory and Applications of Spline Functions (Proceedings of Seminar, Math. Research Center, Univ. of Wisconsin, Madison, Wis., 1968) pp. 157-207 Academic Press, New York.
Z203.37002; M39 #3202

[2] Norm inequalities for a certain class of $C\sp{\infty }$ functions, Israel J. Math. 10 (1971), 364-372.
Z229.26019; M45 #3661

[3] The elementary cases of Landau's problem of inequalities between derivatives, Amer. Math. Monthly, 80 (1973), no. 2, 121-158.
Z261.26014; M47#3619; R1973,8B56

[4] Cardinal spline interpolation. Conference Board of the Mathematical Sciences Regional Conference Series in Applied Mathematics, No. 12. Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1973. vi+125 pp.
Z264.41003; M54 #8095

[5] Cardinal spline interpolation and the exponential Euler splines. Functional analysis and its applications (Internat. Conf., Eleventh Anniversary of Matscience, Madras, 1973; dedicated to Alladi Ramakrishnan), pp. 477-489. Lecture Notes in Math., Vol. 399, Springer, Berlin, 1974.
Z295.41007; M52 #14760; R1975,5B80

[6] On the remainders and the convergence of cardinal spline interpolation for almostperiodic functions. Studies in spline functions and approximation theory, pp. 277-303. Academic Press, New York, 1976.
Z338.41007; M58 #1838

SCHOENEBERG B.,
[1] Elliptic modular functions. Springer-Verlag, New York-Heidelberg, 1974. viii + 233 pp.
Z285.10016; M54#236; R1975,5A640K

SCHOENFELD L.: see BERNDT B.C., SCHOENFELD L.

SCHOFF R.,
[1] The structure of the minus class groups of abelian number fields. University of Utrecht, Preprint No. 588, Oct. 1989.

SCHOISSENGEIER J.,
[1] Der numerische Wert gewisser Reihen, Manuscr. Math., 38 (1982), no. 2, 257-263.
Z499.10013; M83i:10039; R1983,1A82

[2] Der numerische Wert gewisser Reihen, Lecture Notes in Mathematics, No. 1114, 143-147, Springer-Verlag, Berlin-Heidelberg-New York, 1985.
Z557.10013; R1985,11A129

[3] Abschätzung für $\sum_{n\leq N}B_1(n\alpha)$, Monatsh. Math., 102 (1986), no. 1, 59-77.
Z613.10011; M87j:11020; R1987,3A168

[4] Eine explizite Formel für $\sum_{n \leq X}B_2(\{n\alpha\)$. In: Zahlentheoretische Analysis II. Seminar, 1984-86, pp. 134-138. Lecture Notes in Mathematics No. 1262, Springer-Verlag, Berlin - Heidelberg - New York, 1987.
Z622.10007; M90j:11021; R1988,3A199

SCHOISSENGEIER J.: see also HLAWKA E., SCHOISSENGEIER J., TASCHNER R.

SCHOLL A.J.: see SCHAPPACHER N., SCHOLL A.J.

SCHONBACH D.I.: see NEUMAN C.P., SCHONBACH D.I.

SCHÖNHAGE A.: see ODLYZKO A.M., SCHÖNHAGE A.

SCHRÖDER E.,
[1] Verallgemeinerung von Maclaurins Summenformel und Bernoullische Funktionen, Zürich, 1867.

[2] Neueres über Bernoullische Functionen von natürlicher Ordnungszahl, Verhandl. Gesellschaft deutscher Naturforscher und Ärzte, Bremen, 15. - 20. September 1890, 5-6.
J22.0270.01

SCHOOF R.,
[1] Minus class groups of the fields of the $l$th roots of unity, Math. Comp., 67 (1998), no. 223, 1225-1245.
View or retrieve article
Z980.24860; M98j:11085; R01.07-13A.207

SCHROTH P.,
[1] Characterization of the Bernoulli-polynomials, $\exp$ and $\psi$ by Nörlund's multiplication formula, Period. Math. Hung., 12 (1981), no. 3, 191-204.
Z445.39002; M83j:39001; R1982,3B12

SCHULTZ H.J.,
[1] The sum of the $k$-th power of the first $n$ integers. Amer. Math. Monthly, 87 (1980), no. 6, 478-481.
Z445.05006; M82c:05014; R1981,7B565

SCHUMER P.: A HREF="bernd.html#DASC">see DAMIANOU P., SCHUMER P.

SCHUSTER W.,
[1] Improving Stirling's formula. Arch. Math. (Basel) 77 (2001), no. 2, 170-176.
Z1002.33001; M2002f:33005

SCHÜTZENBERGER M.-P.: see FOATA D., SCHÜTZENBERGER M.-P.

SCHWARTZ L.: see BAKER A.J. et al.

SCHWARZ S.,
[1] Algebraic Numbers, (Slovak), Prague, 1950.
Z41.01104; M14-22f

SCHWATT I.J.,
[1] An Introduction to the Operations with Series, Philadelphia, 1924, (s. W. Sierpinski, Rachunek rózniczkowy, Warszawa, 1947).
J50.0151.01

[2] The sum of like powers of a series of numbers forming an arithmetical progression and the Bernoulli numbers, Mat. sbornik, 39 (1932), no. 4, 134-140.
Z7.07002; J58.0093.01

[3] Finite expressions for the Bernoulli numbers obtained by the actual expansion of trigonometric functions by Maclaurin's theorem, J. Math. Pures Appl. (9), 11 (1932), 143-151.
Z5.01402; J58.0093.02

[4] Independent expressions for the Bernoulli numbers. (Abstract). Bull. Amer. Math. Soc., 27 (1921), 261-262.
J48.0255.10

[5] Independent expressions for the Euler numbers. (Abstract). Bull. Amer. Math. Soc., 27 (1921), 262.
J48.0255.11

[6] Independent expressions for the Euler numbers of Higher Order. (Abstract). Bull. Amer. Math. Soc., 27 (1921), 262.
J48.0255.12

[7] Relations involving the numbers of Bernoulli and Euler (Abstract). Bull. Amer. Math. Soc., 27 (1921), 262.
J48.0255.13

[8] Expressions for the Bernoulli function of order $p$. (Abstract). Bull. Amer. Math. Soc., 27 (1921), 348.
J48.0255.14

[9] The values of $\sum_{k=1}^n\sum_{a=1}^{2k} \tan^p a\pi /(2k+1),\; \sum_{k=1}^\infty \prod_{a=1}^{2k} {\rm ctn}^p a\pi(2k+1)$, and similar forms in terms of Bernoulli and Eulerian numbers. (Abstract). Bull. Amer. Math. Soc., 29 (1923), 151.
J49.0161.08

[10] Expressions for the Euler numbers obtained by expanding $\sec x$ by means of Maclaurin's Theorem. Math. Z., 31 (1930), 151-158.
J55.0135.01

[11] Certain expansions involving the Bernoulli numbers. Giornale di Mat., 67 (1929), 162-167.
J55.0216.03

SCHWERING K.,
[1] Zur Theorie der Bernoulli'schen Zahlen, Math. Ann., 52 (1899), no. 1, 171-173.
J30.0253.01

SCOVILLE R.: see CARLITZ L., SCOVILLE R.

SCZECH R.,
[1] Zur Summation von L-Reihen, Bonner Math. Schriften, 1982, No. 141.
Z492.10035; M84m:12015; R1983,4B134

[2] Eisenstein cocylces for $GL_2 Q$ and values of $L$-functions in real quadratic fields. Comment. Math. Helv., 67 (1992), no. 3, 363-382.
Z776.11021; M93h:11047

[3] Eisenstein group cocyles for $GL_n$ and values of $L$-functions. Invent. Math., 113 (1993), no. 3, 581-616.
Z809.11029; M94j:11049

SEGAL R.S.,
[1] Application of Bernoulli polynomials to the theory of cyclotomic fields, Ph.D. Thesis, MIT, 1965.

[2] Generalized Bernoulli numbers and the theory of cyclotomic fields, Acta. Math., 121 (1968), 48-75.
Z164.05802; M38#133; R1969,3A126

SEIDEL P.L. von,
[1] Über eine einfache Entstehungsweise der Bernoullischen Zahlen und einiger verwandten Reihen, Sitzungs. Akad. Wiss. München, Mat.-Phys. Kl., 7 (1877), 157-187.

Sekine, Chizuru,
[1] Dedekind sums with roots of unity and their reciprocity law. Tokyo J. Math. 26 (2003), no. 2, 485-494.
Z1044.11027; M2004i:11038; R 04.10-13A.179

SELBERG A.: see BRUN V., JACOBSTHAL E., SELBERG A., SIEGEL C.

SELFRIDGE J.L., NICOL C.A., VANDIVER H.S.,
[1] Proof of Fermat's Last Theorem for all prime exponents less than 4002, Proc. Nat. Acad. Sci. U.S.A., 41 (1955), no. 11, 970-973.
Z65.27304; M17-348a; R1956,7085

SELIWANOFF D.,
[1] Lehrbuch der Differenzenrechnung. Leipzig, 1904.
J35.0346.07

SELUCKÝ K., SKULA L.,
[1] Irregular imaginary fields, Arch. Math. (Brno), 17 (1981), 95-112.
Z476.12005; M84a:12015; R1982,2A163

SEREBRENIKOV S.Z.,
[1] Tablitsy pervykh devyanosta chisel Bernulli [Tables of the first ninety Bernoulli numbers]. Zap. Akad. Nauk, Sankt Peterburg, 16 (1905), no. 10, 1-8.
J36.0342.02

[2] Novyi sposob vychisleniya chisel Bernulli [A new method of computation of Bernoulli numbers]. Zap. Akad. Nauk, Sankt Peterburg, 19 (1906), 1-6.
J38.0324.05

SERRA CAPIZZANO S.: see COSTABILE F., GUALTIERI M.I., SERRA CAPIZZANO S.

SERRE J.P.,
[1] Cours d'arithmétique, Paris, 1970, Ch.7.
Z225.12002; M41#138; R1971,7A102K

[2] Formes modulaires et fonctions zêta p-adiques. In: Modular functions of one variable, III, Proc. Internat. Summer School, Univ. Antwerp, Antwerp, 1972, 191-268, Lecture Notes in Math., Vol. 350, Springer, Berlin, 1973.
Z277.12014; M53#7949a; R1974,6A446

[3] Sur le residu de la fonction zêta p-adique d'un corps de nombres, C.R. Acad. Sci., Paris, 287A (1978), 183-188.
Z393.12026; M58#22024; R1979,2A259

SERRET J.-A.,
[1] Sur l'évaluation approchée du produit $1. 2. ... .x$ lorsque $x$ est un très-grand nombre, et sur la formule de Stirling, C.R. Acad. Sci., Paris, 50 (1860), 662-666.

SHAFAREVICH I.R.,
[1] Zeta-function. Lecture Notes 1966/67. (Russian) Moscow State Univ., 1969.
R1969,12A249

[2] Selected chapters of algebra (Russian), Matem. obrazovanie, 1997, no. 2, 3-33.

SHAFAREVICH I.R.: see also BOREVICH Z.I., SHAFAREVICH I.R.

SHAH K.N.,
[1] Explicit formulas for $\sum_{i=1}^ri^r (\equiv S_r)$ and Bernoulli's numbers $B_r$, Vidya, B 15 (1972), no. 2, 106-117.
M52#5552

SHAN ZUN: see BUNDSCHUH P., JI CHUN-GANG, SHAN ZUN

SHANK H.S.: see DICKEY L.J., KAIRIES H.H., SHANK H.S.

SHANK H.S.: see GRANVILLE A., SHANK H.S.

SHANKS D.,
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SHANKS E.B.,
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[2] A finite formula for the Bernoulli numbers, Amer. Math. Monthly, 59 (1952), 496.

SHANNON A.G.,
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SHANNON A.G.: see also HORADAM A.F., SHANNON A.G.

SHANNON A.G.: see also MELHAM R.S., SHANNON A.G.

SHARMA A.,
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SHIRATANI K., IMADA T.,
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SHIRATANI K.: see also ISHIBASHI M., SHIRATANI K.

SHIRATANI K.: see also KANEMITSU S., SHIRATANI K.

SHOJI T.: see AGOH T., SHOJI T.,

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SHUKLA R.N.: see also MISRA S.S., SHUKLA R.N.

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J30.0252.01

SIEBERT H.: see KIMURA N., SIEBERT H.

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SIEGEL C.L.: see also BRUN V., JACOBSTHAL E., SELBERG A., SIEGEL C.

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SIMONDS E.F.,
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SINGH A.: see GANDHI J.M., SINGH A.

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SINGH R., PRASAD S.,
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SINGH S.N.,
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SINGH S.N., MISHRA S.S.,
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SINGH S.N., RAI B.K., RAI V.S.,
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SINGH S.N., SINGH V.P., RAI B.K.,
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SINGH S.N.: see also RAI B.K. et al.

SINGH V.P.: see SINGH S.N., SINGH V.P., RAI B.K.

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SITARAMACHANDRA RAO R.: see KANEMITSU S., SITARAMACHANDRA RAO R.

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

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

SKULA L.: see also SELUCKÝ K., SKULA L.

SLAVUTSKII I.SH.,
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[3] On Euler numbers modulo powers of two. J. Number Theory 115 (2005), no. 2, 371-380.
M2006f:11018

[4] Explicit congruences for Euler polynomials. Number theory, 205--218, Dev. Math., 15, Springer, New York, 2006.
M2007a:11025

Sun, Zhi-Wei; Pan, Hao,
[1] Identities concerning Bernoulli and Euler polynomials. Acta Arith. 125 (2006), no. 1, 21--39.

SUN ZHI-WEI: see also GRANVILLE A., SUN ZHI-WEI

SUNSERI R.F.,
[1] Zeros of p-adic L-functions and densities relating to Bernoulli numbers, Ph.D. Thesis, Univ. of Illinois at Urbana-Champaign, 1979.

SUNDARAM S.,
[1] Plethysm, partitions with an even number of blocks and Euler numbers. Formal power series and algebraic combinatorics (New Brunswick, NJ, 1994), 171--198, DIMACS Ser. Discrete Math. Theoret. Comput. Sci., 24, Amer. Math. Soc., Providence, RI, 1996.
Z845.05100; M97c:05162

SURY B.,
[1] The value of Bernoulli polynomials at rational numbers. Bull. London Math. Soc., 25 (1993), no. 4, 327-329.
Z807.11014; M94g:11018; R1995,3A64

[2] Values of Euler polynomials. C. R. Math. Acad. Sci. Soc. R. Can. 23 (2001), no. 1, 12-15.
Z0977.11010; M2001k:11030

SUTTON J.R.,
[1] A series related to Bernoulli's numbers, Nature, 66 (1902), 492.
J33.0291.02

SWINNERTON-DYER H.P.F.,
[1] On $l$-adic representations and congruences for coefficients of modular forms. In: Modular functions of one variable, III (Proc. Int. Summer School, Univ. Antwerp, 1972), pp. 1-55. Lecture Notes in Math., Vol. 350, Springer-Verlag, Berlin, 1973.
Z267.10032; M53#10717a; R1974,6A443

SYLVESTER J.J.,
[1] Note on the numbers of Bernoulli and Euler, and a new theorem concerning prime numbers, Phil. Magaz., 21 (1861), 127-136.

[2] Sur une properiété de nombres premiers qui se rattache au dernier théorème de Fermat, C.R. Acad. Sci., Paris, 52 (1861), 161-163.

[3] Addition à la précédente note, C.R. Acad. Sci., Paris, 52 (1861), 212-214.

[4] Note relative aux communications faites dans les séances des 28 Janvier et 4 Fèvrier 1861, C.R. Acad. Sci., Paris, 52 (1861), 307-308.

SZÁSZ O.,
[1] Über die Approximation stetiger Funktionen durch Bernoullische Polynome, J. Reine Angew. Math., 148 (1918), 183-188.
J46.0420.02

SZEGÖ G.: see POLYA G., SZEGÖ G.

SZENES, A.,
[1] Iterated residues and multiple Bernoulli polynomials, Internat. Math. Res. Notices 1998, no. 18, 937-956.
Z990.19296; M2000m:11022

[2] Residue theorem for rational trigonometric sums and Verlinde's formula. Duke Math. J. 118 (2003), no. 2, 189-227.

SZMIDT J., URBANOWICZ J.,
[1] Some new congruences for generalized Bernoulli numbers of higher orders, preprint, 30pp.

SZMIDT J., URBANOWICZ J., ZAGIER D.,
[1] Congruences among generalized Bernoulli numbers. Acta Arith., 71 (1995), no. 3, 273-278.
Z829.11011; M96f:11032; R1996,4A75

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