Bernoulli Bibliography

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RAAB W.,
[1] Teilbarkeitseigenschaften verallgemeinerter Tangentialkoeffizienten, J. Reine Angew. Math., 241 (1970), 7-14.
Z192.39002; M41#3409; R1970,7A122

RAABE J.L.,
[1] Die Differenzial- und Integralrechnung mit Functionen einer Variablen, Orell, Füssli & Cie., Zürich, 1839, Bd. 1.

[2] Angenäherte Bestimmung der Factorenfolge $1 \cdot 2 \cdots n = \Gamma (1+n) = \int x^n e^{-x}dx$, wenn n eine sehr grosse Zahl ist, J. Reine Angew. Math., 25 (1843), 146-159.

[3] Angenäherte Bestimmung der Function \Gamma (1+n) = \int_0^{\infty} x^n e^{-x}dx$, wenn $n$ eine ganze, gebrochene, oder incommensurable sehr grosse positive Zahl ist, J. Reine Angew. Math., 28 (1844), 10-18.

[4] Die Jacob Bernoullische Funktion, Zürich, 1848.

[5] Zurückführung einiger Summen und bestimmter Integrale auf die Jacob Bernoulli'sche Funktion, J. Reine Angew. Math., 42 (1851), 348-367.

[6] Mathematische Mittheilungen (2 volumes), Zürich, Verlag von Meyer & Zeller, 1857, 1858.

RADEMACHER H.,
[1] Topics in analytic number theory, Springer-Verlag, Berlin, 1973.
Z253.10002; M51#358; R1973,11A116K

RADEMACHER H., GROSSWALD E.,
[1] Dedekind sums. The Math. Assoc. of America, Washington, D.C., 1972. xvi + 102 pp.
Z251.10020; M50#9767; R1973,11A116K

RADICKE A.,
[1] Solutions des questions proposées, Nouv. Corres. Math., 5 (1879), 33; 6 (1880),69-72.

[2] Extrait d'une lettre, Nouv. Corres. Math., 5 (1879), 196.

[3] Démonstration d'un théorème de Stern, Nouv. Corres. Math., 6 (1880), 507-509.
J12.0194.02

[4] Die Recursions-formeln für die Berechung der Bernoullischen und Eulerschen Zahlen, Louis Nebert, Halle a.S., 1880, 35 pp.
J12.0193.01

[5] Démonstration du théorème de Staudt et de Clausen, Nouv. Corres. Math., 6 (1880), 503-507.
J12.0194.01

[6] Zur Theorie der Eulerschen Zahlen, J. Reine Angew. Math., 89 (1880), 257-261.
J12.0193.02

RADO R.,
[1] A new proof of a theorem of v. Staudt, J. London Math. Soc., 9 (1934), 85-88.
J60.0115.02; Z60.0115.02

[2] A note on the Bernoullian numbers, J. London Math. Soc., 9 (1934), 88-90.
J60.0115.03; Z9.15004

RAHMAN, M.: see ISMAIL M.E.H., RAHMAN, M.

RAI B.K., RAI N., SINGH S.N.,
[1] On generalized Bernoulli and Euler polynomials, Bull. Math. Soc. Sci. Math. R.S. Roumanie (N.S.), 25(73) (1981), no. 3, 307-311.
Z475.33009; M83e:33008; R1982,7B29

RAI B.K., SINGH S.N.,
[1] On the extension of Bernoulli and Euler polynomials, Proc. Nat. Acad. Sci. India A, 52 (1982), no. 2, 207-216.
Z514.05006; M85a:33018; R1984,2B43

[2] Properties of some extended Bernoulli and Euler polynomials, Fibonacci Quart., 21 (1983), no. 3, 162-173.
Z529.10016; M85f:05005

RAI B.K.: see also SINGH S.N. et al.

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

RAI V.S., SINGH S.N.,
[1] Certain properties of extended Euler and Bernoulli polynomials, Tamkang J. Math., 16 (1985), no. 4, 1-12.
Z598.10025; M87f:11016; R1987,3A133

[2] A two-variable generalization of Bernoulli and Euler polunomials (Hindi). Vijnana Parishad Anusandhan Patrika, 29 (1986), no. 1, 27-34.
M88j:33013

[3] On extended Bernoulli and Euler polynomials, Proc. Nat. Acad. Sci. India, A 57 (1987), no. 4, 411-426.
Z673.10009; M90h:05016; R1989,3B22

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

RAMACHANDRA K., SANKARANARAYANAN A.,
[1] A remark on ${\zeta}(2n)$, Indian J. Pure Appl. Math., 18 (1987), no.10, 891-895.
Z635.10036; M89a:11087; R1988,6A108

RAMAKRISHNAN B., THANGADURAI R.,
[1] A note on certain divisibility properties of the Fourier coefficients of normalized Eisenstein series. Expo. Math. 21 (2003), no. 1, 75-82.
M2004d:11031

RAMAKRISHNAN D.,
[1] Regulators, algebraic cycles and values of $L$-functions. Algebraic $K$-theory and algebraic number theory, Proc. Semin., Honolulu/Hawaii 1987, Contemp. Math., 83 (1989), 183-310.
Z694.14002; M90e:11094

RAMANUJAN S.,
[1] Some properties of Bernoulli's numbers, J. Indian Math. Soc., 3 (1911), 219-234.
J42.0460.02

[2] Collected Papers, Cambridge Univ. Press, Cambridge, 1927, xxxvi + 355 pp.; reprinted: Chelsea Publ., New York, 1962.
J53.0030.02

[3] Notebooks vol. 1, 2, Tata Inst. Fundamental Research, Bombay, 1957.
M20#6340

RAMARÉ, O.,
[1] Approximate formulae for $L(1,\chi)$. Acta Arith. 100 (2001), no. 3, 245-266.

RANDRIANARIVONY A.,
[1] Fractions continues, $q$-nombres de Catalan et $q$-polynomes de Genocchi. (French) [Continued fractions, $q$-Catalan numbers and $q$-Genocchi polynomials] European J. Combin. 18 (1997), no. 1, 75-92.
Z872.05001; M98e:05007

RANDRIANARIVONY A., ZENG JIANG,
[1] Sur une extension des nombres d'Euler et les records des permutations alternantes. Séminaire Lotharingien de Combinatoire (Gerolfingen, 1993), 97-110, Prépubl. Inst. Rech. Math. Av., 1993/34, Univ. Louis Pasteur, Strasbourg, 1993.
M95j:05023

[2] Sur une extension des nombres d'Euler et les records des permutations alternantes, J. Combin. Theory A, 68 (1994), no. 1, 86-99.
Z809.05002; M95k:05011

[3] Une famille de polynômes qui interpole plusieurs suites classiques de nombres. Séminaire Lotharingien de Combinatoire (Saint Nabor, 1993), 103-126, Prépubl. Inst. Rech. Math. Av., 1994/21, Univ. Louis Pasteur, Strasbourg, 1994.
M95m:11020

[4] Une famille de polynomes qui interpole plusieurs suites classiques de nombres. Adv. in Appl. Math. 17 (1996), no. 1, 1-26.
Z874.05005; M97e:05009

[5] Some equidistributed statistics on Genocchi permutations. The Foata Festschrift. Electron. J. Combin. 3 (1996), no. 2, Research Paper 22, approx. 11 pp. (electronic).
Z857.05002; M97k:05012

RANDRIANARIVONY A.: see also DUMONT D., RANDRIANARIVONY A.

RANDRIANARIVONY A.: see also HAN G.-N.; RANDRIANARIVONY A.; ZENG J.

RANKIN R.A.,
[1] Modular forms and functions. Cambridge Univ. Press, Cambridge-New York-Melbourne, 1977. xiii + 384 pp.
Z376.10020; M58#16518; R1979,1A509

[2] On certain meromorphic modular forms, Analytic number theory, Vol. 2 (Allerton Park, IL, 1995), 713-721, Progr. Math., 139, Birkhäuser Boston, Boston, MA, 1996.
Z862.11032; M97f:11034

RASSIAS T.M.: see HARUKI H., RASSIAS T.M.

RATCLIFFE J.G., TSCHANTZ S.T.,
[1] Volumes of integral congruence hyperbolic manifolds, J. Reine Angew. Math. 488 (1997), 55-78.
Z873.11031; M99b:11076

RAY G.A.,
[1] Relations between Mahler's measure and values of L-series, Canad. J. Math., 39 (1987), no. 3, 694-732.
Z
621.12005; M88m:11071; R1988,4A87

RAY N.,
[1] Extensions of umbral calculus I: Penumbral coalgebras and generalized Bernoulli numbers, Adv. Math., 61 (1986), no. 1, 49-100.
Z
631.05002; M88b:05019; R1987,3A422

[2] Stirling and Bernoulli numbers for complex oriented homology theory. In: G. Carlsson et al. (Eds.), Algebraic Topology (Arcata, CA, 1986), 362-373, Lecture Notes in Math., 1370, Springer-Verlag, Berlin-New York, 1989.
Z
698.55002; M90f:55010; R1990,5A525

[3] Universal constructions in umbral calculus. Mathematical essays in honor of Gian-Carlo Rota (Cambridge, MA, 1996), 343-357, Progr. Math., 161, Birkhäuser Boston, Boston, MA, 1998.
Z
908.05010; M99e:05015

RAY N.: see BAKER A.J. et al.

RAZAR M.J.: see GOLDSTEIN L.J., RAZAR M.J.

RECKNAGEL W.,
[1] Über eine Vermutung von S. Chowla and H. Walum, Arch. Math., 44 (1985), no.4, 348-354.
Z556.10032; M86i:11051; R1985,10A126

[2] Über eine zum Kreisproblem verwandte Summe, Monatsh. Math., 100 (1985), no. 4, 293-298.
Z568.10024; M87b:11083; R1986,5A138

[3] Über eine Verallgemeinerung des Problems von Chowla und Walum, Arch. Math., 46 (1986), no. 2, 148-152.
Z588.10050; M87g:11114; R1986,9A84

[4] Über ein Analogon zu einem Satz von Walfisz, Comm. Math. Univ. St. Paul., 36 (1987), no. 1, 13-20.
Z629.10033; M88f:11099; R1988,9A133

REDFERN E.J.: see ALLENBY R.B.J.T., REDFERN E.J.

REECE M.: see MURTY M. RAM, REECE M.

REICHERT M.A.,
[1] Détermination explicite des courbes elliptiques ayant un groupe de torsion non trivial sur des corps de nombres quadratiques sur Q. Séminaire de théorie des nombres, Univ. Bordeaux I, année 1983-84, exp. no. 11, 33 pp.
Z562.14009; M86h:11049

REMMERT R.: see EBBINGHAUS H.-D. et al.

REMOROV P.N.,
[1] On Kummer's theorem. (Russian) Leningrad. Gos. Univ. Uch. Zap. Ser. Mat. Nauk., 144(23) (1952), 26-34.
M18-381b

[2] Ob otsenke chisla klassov krugovogo polya [On an estimation of the class number of a cyclotomic field]. XXVII Gertsenovsk. chteniya, Matematika, Nauchn. Dokl., Leningrad, 1974, 19-22.
R1974,10A165

RENFER H.,
[1] Die Definitionen der Bernoullischen Funktion und Untersuchung zur Frage, welche von denselben für die Theorie die zutreffendste ist. Inaugural Dissertation, Bern, 1900, 100pp.
J31.0437.01

REVA: see PRABHAKAR T.R., REVA

REY PASTOR J.,
[1] Polinomios correlativos de los de Bernoulli. Boletín Seminario mat. Argentino, 1 (1929), 1-10.
J55.0798.04

RIBENBOIM P.,
[1] Recent results on Fermat's Last Theorem, Canad. Math. Bull., 20 (1977), no. 2, 229-242.
Z355.10015; M57#3050; R1978,5A132

[2] Some criteria for the first case of Fermat's last theorem, Tokyo J. Math., 1 (1978), 149-155.
Z381.10012; M58#10723; R1979,2A132

[3] Fermat's last theorem: recent developments. Sémin. Théor. Nombres, 1978-79, Exp. No. 17, 22 pp., CNRS, Talence, 1979.
Z418.10022; M81m:10025

[4] 13 Lectures on Fermat's Last Theorem, Springer-Verlag, New York- Heidelberg-Berlin, 1979.
Z456.10006; M81f:10023; R1980,8A113K

[5] Fermat's last theorem: Recent developments. Jahrbuch Überblicke Math., 1980, pp. 75-92. Bibliographisches Institut, Mannheim, 1980.
Z458.10016; M82h:10023

[6] The work of Kummer on Fermat's last theorem. Number theory related to Fermat's last theorem (Cambridge Mass., 1981), 1-29, Progr. Math., 26, Birkhäuser, Boston, Mass., 1982.
Z498.12002; M85d:11028; R1985,2A356

[7] Kummer's ideas on Fermat's last theorem, Enseign. Math., 29 (1983), 165-177.
Z521.12002; M85c:01029; R1983,11A6

[8] "1093", Math. Intelligencer, 5 (1983), no. 2, 28-34.
Z516.10001; M85e:11001; R1983,12A100

[9] Krasner versus Fermat, Queen's Mathematical Preprint No. 1983-11 (Kingston, Ont., Canada), 8 pp.

[10] Il mondo Krasneriano, Queen's Mathematical Preprint No. 1983-12 (Kingston, Ont., Canada), 158 pp.

[11] A história do último teorema de Fermat (Portuguese)(The history of Fermat's last theorem), Bol. Soc. Paran. Mat. (2), 5 (1984), no. 1, 14-32.
Z545.10002; M85m:01009; R1985,7A16

[12] Impuissants devant les puissances, Exposition. Math. 6 (1988), no. 1, 3-28.
Z635.10013; M89c:11045

[13] Prime number records (a new chapter for the Guinness Book of Records).(Russian), Uspekhi Mat. Nauk, 42 (1987), no. 5 (257), 119-176.
Z642.10002; M89c:11181; R1988,2A105

[14] The book of prime number records. Springer-Verlag, New York-Berlin, 1988. xxiv + 476 pp.
Z642.10001; M89e:11052; R1989,4A50

[15] The Little Book of Big Primes. Springer-Verlag, New York etc., 1991, xvii+237pp.
Z734.11001; M92i:11008; R1991,8A159

[16] Prime number records. (Spanish) Translated from the English by V. S. Albis Gonzalez. Lect. Mat. 12 (1991), no. 1-3, 137-158.
Z817.11003; M94j:11008

[17] Prime number records. Nieuw Arch. Wisk. (4), 12 (1994), no. 1-2, 53-65.

[18] The new book of prime number records. Springer-Verlag, New York, 1996. xxiv+541 pp.
Z856.11001; M96k:11112

[19] Classical theory of algebraic numbers. Universitext. Springer-Verlag, New York, 2001. xxiv+681 pp.
M2002e:11001

[20] My numbers, my friends. Popular lectures on number theory. Springer-Verlag, New York, 2000. xii+375 pp.
Z947.11001; M2002d:11001

RIBET K.A.,
[1] A modular construction of unramified p-extensions of $Q(\mu_p)$, Inventiones Math., 34 (1976), no. 3, 151-162.
Z338.12003; M54#7424; R1977,6A253

[2] p-adic L-functions attached to characters of p-power order, Sémin. Delange-Pisot-Poitou, Théorie des Nombres, 19e année, 1977/1978, Exp. no. 9, 8pp.
Z394.12007; M80b:12012; R1979,7A393

[3] Fonctions L p-adiques et théorie d'Iwasawa (Notes by Ph. Satgé), Publ. Math. d'Orsay, Univ. Paris-Sud, Départ. Math., 1979.
Z445.12007; M81c:12022

[4] Report on p-adic L-functions over totally real field, Journées Arithmétiques de Luminy, Astérisque, Soc. Math. France, Paris, 61 (1979), 177-192.
Z408.12016; M81f:12009; R1979,10A233

[5] Sur la recherche des p-extensions non ramifiées de $Q(\mu_p)$, Groupe étude algèbre, Univ. P. et M. Curie, (1975-76), 1 (1978), no. 2, 1-3.
Z375.12007; M80f:12005; R1978,11A406

RIBET K.A.: see also DELIGNE P., RIBET K.A.

RICCI G.,
[1] Un perfezionamento dei teoremi di Sylvester, N. Nielsen, Saalschütz, Lipschitz sui numeri di Bernoulli, Giorn. di Mat. Battaglini, 69 (1931), 1-4.
J57.0179.03; Z2.17803

[2] Sui coefficienti binomiali e polinomiali. Una dimonstrazione del teorema di Staudt-Clausen sui numeri di Bernoulli, Giorn di Mat. Battaglini, 69 (1931) 9-12.
J57.0180.01; Z2.17901

RICCI P.E.: see BRETTI G, RICCI P.E.

RICCI P.E.: see also BRETTI G., NATALINI P., RICCI P.E.

RICCI P.E.: see DI CAVE A., RICCI P.E.

RIEGER G.I.,
[1] Eine Bemerkung über die Hurwitzschen Zahlen, J. Reine Angew. Math., 296 (1977), 212-216.
Z375.12007; M56#15550; R1978,8A112

TE RIELE H.J.J.: see IVIC A., TE RIELE H.J.J.

TE RIELE H.J.J.: see MOREE P., TE RIELE H.J.J., URBANOWICZ J.

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

RIESEL H.,
[1] Om rekursionsformuler för Bernoullis Tal, Nordisk Matem. Tidskrift, 9 (1961), 44-48, 95-96.
Z116.26701; M23#A3101; R1962,6A106

[2] Bernoullis tal och von Staudts teorem, Elementa, 51 (1968), no. 3, 201-206.
R1969,4A69

[3] Some series related to infinite series given by Ramanujan, Nordisk. Tidsk. Informationsbehandling (BIT), 13 (1973), 97-113.
Z252.10040; M50#820; R1973,9B27

[4] A consequence of the von Staudt - Clausen theorem, Nordisk. Tidskr. Informationsbehandling (BIT), 14 (1974), 120-121.
Z271.10004; M49#199; R1974,8A113

[5] An "exact" formula for the $2n$-th Bernoulli number, Acta Arith., 26 (1975), 273-277.
Z271.10009; M51#10214; R1976,2A159

RIM SEOGHOON: see JANG LEE-CHAE, KIM TAEKYUN, RIM SEOGHOON, SON JIN-WOO

RIM SEOG-HOON: see also JANG LEE CHAE, PAK HONG KYUNG, RIM SEOG-HOON, PARK DAL-WON

RIM SEOG-HOON: see also KIM TAEKYUN, JANG LEE CHAE, RIM SEOG-HOON, PAK HONG-KYUNG

RIM SEOG-HOON: see also KIM TAEKYUN, RIM SEOG-HOON

RIM SEOGH-HOON: see also PAK HONG-KYUNG, RIM SEOGH-HOON.

RIMSKII-KORSAKOV B.S.,
[1] Zametka ob obobshchennykh teoremakh umnozheniya bernullievykh polinomov i kinkelinovykh funktsij [A note on the generalized multiplication theorems for Bernoulli polynomials and Kinkelin functions]. Trudy. Moskovsk. aviatsionnogo instituta, 1947, no. 6, 49-52.

RIORDAN J.,
[1] Inverse relations and combinatorial identities, Amer. Math. Monthly 71 1964, 485-498.
Z128.01603; M30#34; R1965,3A137

[2] Combinatorial identities. John Wiley & Sons, Inc., New York- London-Sidney, 1968. xiii $+$256pp. Reprint Robert E. Krieger Publ. Co., Huntington, N.Y., 1979.
Z194.00502; M38#53; R1970,3V264K

RIORDAN J., STEIN P.R.,
[1] Proof of a conjecture on Genocchi numbers, Discrete Math., 5 (1973), no. 4, 381-388.
Z271.05004; M47#4919; R1974,1V304

RIORDAN J.: see also CARLITZ L., RIORDAN J.

RITTER J., WEISS A.,
[1] Cohomology of units and $L$-values at zero, J. Amer. Math. Soc. 10 (1997), no. 3, 513-552.
Z885.11059; M98a:11150

Rivoal, Tanguy,
[1] Nombres d'Euler, approximants de Padé et constante de Catalan. Ramanujan J. 11 (2006), no. 2, 199-214.

ROBBINS N.,
[1] Revisiting an old favourite: $\zeta(2m)$, Math. Mag. 72 (1999), no. 4, 317-319.

[2] Some arithmetic properties of Bernoulli numbers. JP J. Algebra Number Theory Appl. 5 (2005), no. 1, 201-204.
M2006a:11023

ROBBINS N.: see also KNOPFMACHER A., ROBBINS N.
ROBERT A.M.,
[1] A note on the numerators of the Bernoulli numbers. Exposition. Math., 9 (1991), no. 2, 189-191.
Z738.11024; M92c:11017; R1991,12A67

[2] A course in $p$-adic analysis. Graduate Texts in Mathematics, 198. Springer-Verlag, New York, 2000. xvi+437 pp.
Z947.11035; M2001g:11182

ROBERT G.,
[1] Nombres de Hurwitz et régularité des idéaux premiers. Séminaire Delange - Pisot - Poitou (16e année: 1974/75), Fasc. 1, Exp. No. 21, 7 pp., Paris, 1975.
Z372.12011; M53#348; R1976,7A447

[2] Nombres de Hurwitz et unités elliptiques, Ann. Sci. École Norm. Sup. (4), 11 (1978), no. 3, 297-389.
Z409.12008; M80k:12010; R1979,8A360

RODRIGUEZ D.M.: see DEEBA E.Y., RODRIGUEZ D.M.

RODRIGUEZ VILLEGAS F.,
[1] The congruences of Clausen - von Staudt and Kummer for half-integral weight Eisenstein series. Math. Nachr., 162 (1993), 187-191.
Z805.11042; M94h:11048

RÖDSETH Ö. J.,
[1] A note on Brown and Shiue's paper on a remark related to the Frobenius problem, Fibonacci Quart., 32 (1994), no.5, 407-408.
Z840.11009; M95j:11022; R1997,11A154

ROGEL F.,
[1] Ueber den Zusammenhang der Facultäten-Coefficienten mit den Bernoullischen und Eulerschen Zahlen, Arch. Math. und Phys. (2), 10 (1891), 318-332.
J23.0272.01

[2] Arithmetische Entwickelungen, Arch. Math. und Phys. (2), 11 (1892), 77-84.
J24.0185.02

[3] Ein neues Recursionsgesetz der Bernoullischen Zahlen, Sitzungsb. Kgl. Böhmische Gesells. Wiss., Prag, (1895), No. 26, 1-4.
J26.0286.01

[4] Die Entwickelung nach Bernoullischen Funktionen, Sitzungsb. Kgl. Böhmische Gesells. Wiss., Prag, (1896), No. 31, 1-48.
J27.0329.06

[5] Die Entwickelung nach Bernoulli'schen Functionen, Arch. Math. und Phys. (2), 17 (1899), 129-146.
J30.0251.02

[6] Question 13781, Math. questions and solutions from "Educational Times", London, 70 (1899), 37-38.
J30.0250.01

[7] Question 13868, Math. questions and solutions from "Educational Times", London, 70 (1899), 121-122.
J30.0250.02

[8] Question 14066, Math. questions and solutions from "Educational Times", London, 71 (1899), 34-35.
J30.0250.03

[9] Question 13959, Math. questions and solutions from "Educational Times", London, 71 (1899), 126-128.
J30.0251.01

[10] Question 14194, Math. questions and solutions from "Educational Times", London, 72 (1900), 125-126.
J31.0287.02

[11] Über Bernoullische und Eulersche Zahlen (Czech), Sitzungsber. d. kgl. Böhmischen Gesells. Wiss., Prag, (1907), No. 23, 1-27.
J38.0316.01

[12] Theorie der Euler'schen Functionen. Sitzungsber. d. kgl. Böhm. Ges. Wiss., (1896), no. 2, 45p.
J27.0333.01

[13] Note zur Entwickelung nach Euler'schen Funktionen. Sitzungsber. d. kgl. Böhm. Ges. Wiss., Prag., (1896), no. 42, 1-9.
J27.0329.07

[14] Transformationen der harmonischen Reihen $S_{2n+1}$ und $U_{2n}$. Sitzungsber. d. kgl. Böhm. Ges. Wiss., Prag., (1907), no. 17, 14p.
J38.0316.02

ROMAN S.,
[1] The umbral calculus, New York, Acad. Press Inc., (Pure and Appl. Math., 111 ) 1984.
Z536.33001; M87c:05015

ROMANOV N.P.,
[1] On an orthogonal system., Doklady Akad. Nauk SSSR (N.S.), 40 (1943), 257-258.
M6-49a

[2] On Hilbert space and the theory of numbers, II. (Russian) Izv. Akad. Nauk. SSSR. Ser. Mat., 15 (1951), 131-152.
Z44.04002; M13-208g

[3] Ob odnom novom analiticheskom predstavlenii dzeta-funktsii Rimana [On a new analytical representation of the Riemann zeta function]. Trudy Sredneaz. Univ., (1956), vyp. 66, kn. 13, 51-54.
R1957,56

ROSE H.E.,
[1] A course in number theory. The Clarendon Press, Oxford University Press, New York, 1988. xii + 354 pp.
Z637.10002; M89f:11002

ROSELLE D.P.: see DILLON J.F., ROSELLE D.P.

ROSEN K.H. (Editor-in-Chief),
[1] Handbook of discrete and combinatorial mathematics. CRC Press, Boca Raton, FL, 2000. xiv+1232 pp.
M2000g:05001

ROSEN K.H., SNYDER W.M.,
[1] A Kummer congruence for the Hurwitz-Herglotz Function, Tokyo J. Math., 6 (1983), no. 1, 125-138.
Z523.10006; M84m:10018; R1984,2A432

[2] p-adic Dedekind sums, J. Reine Angew. Math., 361 (1985), 23-26.
Z561.10005; M87b:11037; R1986,4A396

ROSEN M.,
[1] Remarks on the history of Fermat's Last Theorem 1844 to 1984. Cornell, Gary (ed.) et al., Modular forms and Fermat's last theorem. Papers from a conference, Boston, MA, USA, August 9-18, 1995. New York, NY: Springer, 505-525 (1997).
Z893.11011

ROSEN M.: see also IRELAND K., ROSEN M.

ROSENHEAD L.: see FLETCHER A. et al.

ROSSI F.S., TOSCANO L.,
[1] Sui polinomi e sui numeri di Bernoulli e di Eulero, Archimede, 20 (1968), no. 3, 155-160.
Z165.36101; M38#2354; R1969,2V204

ROTA G.-C.,
[1] Combinatorial snapshots, Math. Intelligencer 21 (1999), no. 2, 8-14.

ROTA G.-C., TAYLOR B.D.,
[1] An introduction to the umbral calculus. Analysis, geometry and groups: a Riemann legacy volume, 513-525, Hadronic Press, Palm Harbor, FL, 1993.
Z910.05010; M96a:05015

[2] The classical umbral calculus, SIAM J. Math. Anal., 25 (1994), no. 2, 694-711.
Z797.05006; M95d:05014

ROTA G.-C.: see also DI CRESCENZO, ROTA G.-C.

ROTHE H.A.,
[1] Relationen der Lokalausdrücke von Potenzen besonderer merkwürdiger Reihen. In: K. F. Hindernburg, Sammlung combinatorisch-analytischer Abhandlungen, 2-te Sammlung, G. Fleischer, Leipzig, 1800.

[2] Bekanntmachung für Mathematiker, Allgemeine Literatur-Zeitung, Halle, Bd. 1, No. 63 (1817), 503-504.

ROUGH M.,
[1] Some numbers related to the Bernoulli numbers, Math. Mag., 29 (1955), 101-103.
R1956,6352

ROVINSKY M.,
[1] Multiple gamma functions and $L$-functions. Math. Res. Lett. 3 (1996), no. 5, 703--721.
Z867.11061; M98b:11093

ROY Y.: see CARTIER P., ROY Y.

RUBIN K.,
[1] Congruences for special values of L-functions of elliptic curves with complex multiplication, Invent. Math., 71 (1983), no. 2 339-364.
Z513.14012; M84h:12018; R1983,7A409

[2] The main conjecture. Appendix to: Cyclotomic Fields by S. Lang, 2nd ed., Springer-Verlag, New York, 1990.
M91c:11001

[3] Kolyvagin's system of Gauss sums. Proc. Conf., Texel/Neth. 1989, Prog. Math., 89 (1991), 309-324.

RUBIN K.: see also LANG S. [7]

RUBIN K., WILES A.,
[1] A Mordell-Weil group of elliptic curves over cyclotomic fields. Number theory related to Fermat's last theorem (N. Koblitz, Ed.), Progress in Math., No. 26, Birkhäuser, Boston, Mass., 1982, 237-254.
Z519.14017; M84h:12017; R1986,4A396

Rubinstein, Boris Y.; Fel, Leonid G.,
[1] Restricted partition functions as Bernoulli and Eulerian polynomials of higher order. Ramanujan J. 11 (2006), no. 3, 331--347.

RUDAZ S.,
[1] Note on asymptotic series expansions for the derivative of the Hurwitz zeta function and related functions. J. Math. Phys., 31 (1990), no. 12, 2832-2834.
Z729.11043; M91j:33012

RUDOLFER S.M., WILKINSON K.M.,
[1] A number-theoretic class of weak Bernoulli transformations, Math. Systems Theory, 7 (1973), 14-24.
Z258.10031; M48#2100; R1974,1V47

RUIJSENAARS S.N.M.,
[1] On Barnes' Multiple Zeta and Gamma Functions. Adv. Math. 156 (2000), no. 1, 107-132.
Z0966.33013; M2002b:33022

RUTGERS J.G.,
[1] Over de getallen en de polynomen van Stirling. Handel. Nederl. Natuur- en Geneesk. Congr., 11 (1907), 260-265.
J38.0467.02

RUTKOWSKI J.,
[1] A $p$-adic analogue of the Legendre system. Number Theory, v. 2 (Budapest, 1987), 939-950. Colloq. Math. Soc. Janos Bolyai, 51 Amsterdam, 1990.
Z701.11064; M91h:11134

RUTKOWSKI J.: see also BARTZ K., RUTKOWSKI J.

RYBNIKOV K.A.,
[1] Introduction to combinatorical analysis, Moscow: Moscow State Univ., 1985, 2nd ed., 308 pp.
Z617.05001; M87b:05002; R1985,11V564K

Ryoo, C. S.,
[1] Structure of the zeros of $q$-Bernoulli polynomials. J. Appl. Math. Comput. 17 (2005), no. 1-2, 49-58.
M2005h:11040

Ryoo, Cheon Seoung,
[2] Distribution of the zeros of $q$-Bernoulli polynomials. Int. Rev. Pure Appl. Math. 1 (2005), no. 1, 135--141.
M2006j:11027

[3] A numerical investigation on the zeros of the Genocchi polynomials. J. Appl. Math. Comput. 22 (2006), no. 1-2, 125-132.

RYOO CHEON SEOUNG, KIM TAEKYUN,
[1] Beautiful zeros of $q$-Euler polynomials of order $k$. Proc. Jangjeon Math. Soc. 7 (2004), no. 1, 63-79.
M2005c:11023

Ryoo, C. S.; Kim, T.; Agarwal, R. P.,
[1] Exploring the multiple Changhee $q$-Bernoulli polynomials. Int. J. Comput. Math. 82 (2005), no. 4, 483-493.

[2] The structure of the zeros of the generalized Bernoulli polynomials. Neural Parallel Sci. Comput. 13 (2005), no. 3-4, 371--379.
M2006h:26016

[3] Distribution of the roots of the Euler-Barnes' type $q$-Euler polynomials. Neural Parallel Sci. Comput. 13 (2005), no. 3-4, 381-392.
M2006j:33024

Ryoo, Cheon Seoung; Kim, Taekyun; Park, Dal-Won; Rim, Seog-Hoon,
[1] On the real roots of the Changhee-Barnes' $q$-Bernoulli polynomials. JP J. Algebra Number Theory Appl. 5 (2005), no. 2, 293--305.
M2006k:11033

Ryoo, C. S.; Song, H.,
[1] On the real roots of the Changhee-Barnes' $q$-Bernoulli polynomials. Proceedings of the 15th International Conference of the Jangjeon Mathematical Society, 63--85, Jangjeon Math. Soc., Hapcheon, 2004.
M2005j:11021

RYOO C.S.: see also JANG L.C., KIM J.H., KIM T., LEE D.H., PARK D.W., RYOO C.S.

RYOO C.S.: see also KIM T., JANG L.C., RYOO C.S., PARK D.-W.

RZADKOWSKI G.,
[1] A short proof of the explicit formula for Bernoulli numbers. Amer. Math. Monthly 111 (2004), no. 5, 432-434.
Z1069.11010

[2] Euler-Maclaurin summation and the generalized factorial. Math. Gazette 85 (2001), no. 504, 507-512.


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