Bernoulli Bibliography

T


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TABIRCA S.,
[1] Some remarks concerning the Bernoulli numbers. Notes Number Theory Discrete Math. 6 (2000), no. 2, 29-33.
M2001k:11031

TAKÁCS L.,
[1] On generalized Dedekind sums. J. Number Theory, 11 (1979), no. 2, 264-272.
Z404.10006; M80j:10019; R1979,12A107

TAKAGI T.,
[1] On the law of recipricity in the cyclotomic corpus, Proc. Phys.-Math. Soc. Japan (3), 4 (1922), 173-182.
J48.0169.02

[2] Cuspidal class number formula for the modular curves $X_1(p)$. J. Algebra, 151 (1992), no. 2, 348-374.
Z773.11040; M93g:11063

[3] The cuspidal class number formula for the modular curves $X_1(p^m)$. J. Algebra, 158 (1993), no. 2, 515-549.
M94d:11040

TALBOT R.F.: see BURROWS B.L., TALBOT R.F.

TALL D.O.: see STEWART I.N., TALL D.O.

TAMARKINE J.: see FRIEDMANN A.A., TAMARKINE J.

TAMBS LYCHE R.,
[1] Sur les coefficients du développement de $1/\cos x$ en série entière. Bull. Sci. Math. (2), 50 (1926), 230-236.
J52.0356.07

[2] Bemerkung zu den Formeln von I. J. Schwatt für die Eulerschen Zahlen. Math. Z., 32 (1930), 586.
J56.0872.04

[3] Tillegg til foranstående artikkel (supplement to the previous paper), Nordisk Mat. Tidsskrift, 6 (1958), 159-161, 182.
Z088.02003

TAMME G.,
[1] Über die p-Klassengruppe des p-ten Kreisteilungskörpers, Ber. Math.-Stat. Sekt. Forschungsgesellsch. Joanneum, 1988, no. 299, 1-48.
Z653.12002; M91b:11117; R1988,12A313

TANEJA V.S.: see GANDHI J.M., TANEJA V.S.

TANIGAWA Y.: see AKIYAMA S., EGAMI S., TANIGAWA Y.

TANIGAWA Y.: see also AKIYAMA S., TANIGAWA Y.

TANNER J.W.,
[1] Proving Fermat's last theorem for many exponents by computer. B.A. Thesis, Harvard Univ., 1985.

TANNER J.W., WAGSTAFF S.S., JR.,
[1] New bound for the first case of Fermat's last theorem, Math. Comp., 53 (1989), no. 188, 743-750.
Z694.10018; M90h:11028

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

TANNERY P.,
[1] Introduction à la théorie des fonctions d'une variable, Paris, 1886, Ch. 7.
J18.0328.02

TANTURRI A.,
[1] Dalla formola di Pascal a quella di Bernoulli sulle somme delle potenze simili dei primi $n$ numeri. Periodico di Mat. (3), 5 (1907), 80-83.
J38.0314.03

[2] Un expressione nuova dei numeri Bernoulliani. Rom. Acc. L. Rend. (5), 30 (1921), 44-46.
J48.1194.04

TAO QING SHENG,
[1] Generalizations of Bernoulli polynomials and Euler-Maclaurin formulas (Chinese. English summary). Gaoxiao Yingyong Shuxue Xuebao, 7 (1992), no. 2, 177-183.
Z778.11013

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

TAUBER S.,
[1] Combinatorial numbers in ${\bf C}^n$, Fibonacci Quart. 14 (1976), no. 2, 101-110.
Z352.05005; M53#7795; R1977,3V374

TAUSSKI O., TODD J.,
[1] Some discrete variable computations, Proc. Symp. Appl. Math., 10 (1960), 201-209.
Z96.00503; M22#6063; R1961,9A136

TAYA H.,
[1] Iwasawa invariants and class numbers of quadratic fields for the prime $3$. Proc. Amer. Math. Soc. 128 (2000), no. 5, 1285-1292.
Z 0958.11069; M2000j:11162; R01.03-13A.165

TAYLOR B.D.,
[1] Difference equations via the classical umbral calculus. Mathematical essays in honor of Gian-Carlo Rota (Cambridge, MA, 1996), 397-411, Progr. Math., 161, Birkhäuser Boston, Boston, MA, 1998.
Z903.05007; M99h:39011

TAYLOR B.D.: see ROTA G.-C., TAYLOR B.D.

TAYLOR M.J.: see CASSOU-NOGUÈS PH., TAYLOR M.J.

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

TCHISTIAKOV I.I.: see CHISTYAKOV I.I.

TEIXEIRA F.G.,
[1] Note sur les nombres de Bernoulli, Amer. J. Math., 7 (1885), 288-292.
J17.0231.02

[2] Sur les démonstrations de deux formules pour le calcul des nombres de Bernoulli, Enseign. Math., 7 (1905), 442-446.
J36.0342.01

TEIXEIRA J.P.,
[1] Sur les nombres Bernoulliens, J. Sci. Math., Lisboa, 3 (1893) (1895), 73-75.
J25.0412.01

TEMME N.M.,
[1] Bernoulli polynomials old and new: Problems in complex analysis and asymptotics. Apt, Krzysztof (ed.) et al., From universal morphisms to megabytes: a Baayen space Odyssey. On the occasion of the retirement of Prof. Dr. P. C. Baayen. Amsterdam: CWI, 559-576 (1994).
Z879.11008; M99a:11020

[2] Bernoulli polynomials old and new: generalizations and asymptotics, CWI Quarterly, 8 (1995), no. 1, 47-67.
Z879.11008; M96j:11020

[3] Special Functions. An Introduction to the Classical Functions of Mathematical Physics, John Wiley & Sons, New York, etc., 1996.
Z856.33001; M97e:33002

TEMME N.M.: see also LÓPEZ J.L.; TEMME N.M.

TENENBAUM G.,
[1] Introduction to analytic and probabilistic number theory. Translated from the second French edition (1995) by C. B. Thomas. Cambridge Studies in Advanced Mathematics, 46. Cambridge University Press, Cambridge, 1995. xvi+448 pp. ISBN: 0-521-41261-7
Z831.11001; M97e:11005b

TEPPER M.,
[1] Combinations and sums of powers, Fibonacci Quart. 12 (1974), 196-198.
Z281.10005; M50#4472

TERRILL H.M.,
[1] Methods for computing generalized Euler numbers, Amer. Math. Monthly, 44 (1937), 526-527.
Z17.20402

TERRILL H.M., TERRILL E.M.,
[1] Tables of numbers related to the tangent coefficients, J. Franklin Institute, 239 (1945), 66-67.

TERRY T.R.,
[1] Question 9141, Math. questions and solutions from the "Educat. Times", London, 10 (1906), 70.
J37.0297.02

THACKER A.,
[1] Ein Beitrag zur Zahlentheorie, J. Reine Angew. Math., 40 (1850), 89-92.

[2] Propositions in the theory of numbers, Camb. and Dubl. Math. J., 5 (1850), 243-248.

THAINE F.,
[1] Polinômios que generalizam os coeficientes binomiais e sua aplicaçáo no estudo do último theorema de Fermat, Ph.D. thesis, Rio de Janeiro, 1979, 86 pp.

[2] Polynomials generalizing binomial coefficients and their application to the study of Fermat's last theorem, Fundação Universidade de Brasília, Trabalho de Matemática, No. 156, Nov. 1979, 1-70.

[3] Polynomials that generalize binomial coefficients and their applications to Fermat's last theorem. (Portuguese). Proc. Twelfth Brazilian Math. Coll., Vol. I, II (Poços de Caldas, 1979), pp. 50-64, Rio de Janeiro, 1981.
Z504.10009; M84j:10013

[4] Polynomials generalizing binomial coefficients and their application to the study of Fermat's last theorem, J. Number Theory, 15 (1982), no. 3, 304-317.
Z504.10009; M84d:10023; R1983,8A137

[5] On the first case of Fermat's last theorem, J. Number Theory, 20 (1985), no. 2, 128-142.
Z571.10016; M87d:11021; R1986,2A131

[6] On the ideal class groups of real abelian number fields, Universidade Estadual de Campinas, Sao Paolo, Brasil, Relatorio Interno, No. 355, Jun. 1986, 1-37.

[7] On Fermat's last theorem and the arithmetic of $ Z[\xi_p + \xi_p^{-1}]$, Relatório Técnico, Instituto de Matemática, Universidade Estadual de Campinas, Campinas - Sao Paolo, Brasil, No. 22/87, Jun. 1987, 1-6.

[8] On the ideal class groups of real abelian number fields, Ann. of Math. (2), 128 (1988), no. 1, 1-18.
Z665.12003; M89m:11099; R1989,4A259

[9] On Fermat's last theorem and arithmetic of $ Z[{\zeta}_p + {{\zeta}_p}^{-1}]$, J. Number Theory, 29 (1988), no. 3, 297-299.
Z654.10018; M89m:11029; R1989,1A106

[10] On the relation between units and Jacobi sums in the prime cyclotomic fields. Manuscripta Math., 73 (1991), no. 2, 127-151.
Z760.11030; M92m:11122; R1992,4A298

[11] On the $p$-part of the ideal class group of ${\openQ}(\zeta_p + \zeta^{-1}_p)$ and Vandiver's conjecture. Michigan Math. J., 42 (1995), no. 2, 311-344.
Z844.11069; M96e:11140

THAKARE N.K.,
[1] Generalization of Bernoulli, Euler numbers and related polynomials, Boll. Un. Mat. Ital. B (5), 18 (1981), no. 3, 847-857.
Z475.33010; M83m:05009; R1982,5B55

THAKARE N.K.: see also KARANDE B.K., THAKARE N.K.

THAKUR D.S.,
[1] Zeta measure associated to $F_q[T]$, J. Number Theory, 35 (1990), no. 1, 1-17.
Z703.11065; M91e:11139

THANG LE THU QUAC, MURAKAMI JUN,
[1] On Kontsevich's integral for the Homfly polynomial and relations of fixed Euler numbers. Max-Planck-Institut für Math., Bonn, MPI/93-26, 17 pp.

THANGADURAI R.,
[1] Adams theorem on Bernoulli numbers revisited. J. Number Theory 106 (2004), no. 1, 169-177.
M2005b:11022

THANGADURAI R.: see also RAMAKRISHNAN B., THANGADURAI R.

THIRUVENKATACHARYA V.,
[1] Some properties of Euler's numbers and associated polynomials. J. Indian Math. Soc., 16 (1927), Suppl., 19.
J52.0361.06

THOMAN F.,
[1] Logarithmes des 40 premiers nombres de Bernoulli, C.R. Acad. Sci., Paris, 50 (1860), 905-906.

[2] Développement des séries à termes alternativement positifs et negatifs à l'aide des nombres de Bernoulli, C.R. Acad. Sci., Paris, 64 (1867), 655-659.

THOMAS C.B.,
[1] Cohomology of metacyclic groups and class numbers of subfields of cyclotomic extensions, J. Algebra, 164 (1994), no. 1, 53-84.

Z816.11056; THOMPSON W.J.,
[1] Atlas for computing mathematical functions. An illustrated guide for practioners with programs in C and Mathematica. Incl. 1 CD-ROM. Chichester: Wiley. xiv, 903 p. (1997).
Z873.68100

[2] Atlas for computing mathematical functions: an illustrated guide for practitioners, with program in Fortran 90 and Mathematica. Incl. 1 CD-ROM. Chichester: John Wiley & Sons. xiv, 888 p. (1997).
Z885.68089; M98g:65001

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

TIJDEMAN R.: see GYÖRY K., TIJDEMAN R., VOORHOEVE M.

TITCHMARSH E.C.,
[1] The theory of the Riemann zeta-function, Oxford, Clarendon Press, 1951, vi+346pp. (2nd Ed., 1986, M88c:1049.)
Z42.07901; M13-741c

TITS L.,
[1] Identités nouvelles pour le calcul des nombres de Bernoulli. Nouv. Ann. Math. (5), 1 (1923), 191-196.
J49.0167.01

TODD J.: see TAUSSKI O., TODD J.

TODOROV P.G.,
[1] Une nouvelle représentation explicite des nombres d'Euler, C.R. Acad. Sci., Paris, 286A (1978), no. 19, 807-809.
Z378.10007; M58#27737; R1978,11A89

[2] On a new explicit representation of Euler numbers, Plovdiv Univ. Nauchn.Trud., 16 (1978), no. 1, 259-301 (1980).
M82m:05006

[3] The nth derivative of $tg z$, Plovdiv Univ. Nauchn. Trud., 21 (1983), no. 1, 93-98.
Z599.30042

[4] On the theory of the Bernoulli polynomials and numbers, J. Math. Anal. Appl., 104 (1984), no. 2, 309-350.
Z552.10007; M86h:05020; R1986,1B22

[5] Une formule simple explicite des nombres de Bernoulli généralisés, C.R. Acad. Sci. Paris, Sér. A, 301 (1985), no.13, 665-666.
Z606.10008; M87e:11025

[6] Taylor expansions of certain composite functions, C.R. Acad. Bulgare Sci., 39 (1986), no. 11, 15-18.
Z624.05003; M88b:05009; R1987,6B3

[7] The nth derivative of $tg z$. Functiones et Approximatio, Adam Mickiewicz University Press, Poznán, XV (1986), 171-173.
Z621.33003

[8] On certain formulas for the Stirling numbers of the first and the second kind, Plovdiv. Univ. Nauchn. Trud., 26 (1988), no. 3, 17-23.
Z735.11013

[9] Taylor expansions of analytic functions related to $(1 + z)^x - 1$, J. Math. Anal. Appl., 132 (1988), no. 1, 264-280.
Z646.30002; M89e:30001; R1988,10B148

[10] Recurrence relations for certain polynomials, Facta Univ. Ser. Math. Inform., 4 (1989), 19-26.
Z702.11008; M91g:11019

[11] On certain formulas for the Stirling numbers of the first and the second kind, Punjab Univ. J. Math., 22 (1989-90), 31-35.
Z723.11013; M91f:11011

[12] A disproof of a conjecture of Robertson, Mitt. Math. Ges. Hamburg, 12 (1991), no.2, 495-497.
Z780.30003; M93a:30029

[13] Explicit formulas for the Bernoulli and Euler polynomials and numbers. Abh. Math. Sem. Univ. Hamburg, 61 (1991), 175-180.
Z748.11016; M93b:11019

[14] A disproof of a conjecture of Robertson and generalizations. Punjab Univ. J. Math. (Lahore), 23 (1990), 83-91.
Z734.30019; M92k:30003

[15] A disproof of a conjecture of Robertson and generalizations. Publ. Inst. Mathématique (Beograd) (N.S.) 50, 64 (1991),105-110.
Z780.30002; M94k:30003

[16] Explicit and recurrence formulas for generalized Euler numbers. Funct. Approx. Comment. Math., 22 (1993), 13-17 (1994).
Z827.11011; M95h:11016

[17] Partial fraction decomposition and a new form of the Taylor expansion of the function $(z/(e^z-1))^m$. Funct. Approx. Comment. Math., 23 (1994), 59-67 (1995).
Z873.41030; M96e:11028; R1996,8B252

TODOROV P.G.: see also SRIVASTAVA H.M., TODOROV P.G.

TOLSTIKOV A.V.,
[1] Application of fields generated by Gauss periods to the study of cyclic Diophantine equations. Studies in number theory. 4. Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI), 67 (1977), 201-222, 227.
Z368.10015; M56#2913; R1977,7A159

[2] Application of fields generated by Gauss periods to the study of cyclic Diophantine equations. II. Studies in number theory. 5. Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI), 82 (1979), 149-157.
Z433.10008; M80h:10024; R1979,10A97

TOOLE B.A.: see KIM E.E., TOOLE B.A.

TORNHEIM L.,
[1] Harmonic double series. Amer. J. Math., 72 (1950), 303-314.
Z36.17203; M11-654a

TOSCANO L.,
[1] Successioni ricorrenti e polinomi di Bernoulli e di Eulero, Accad. Sci. Fis. e Mat. Napoli, Rend., IV.S., 6 (1936), 55-61.
J62.1223.04; Z15.25005

[2] Sui coefficienti della tangente e sui numeri di Bernoulli, Boll. Un. Mat. Ital., 15 (1936), 8-12.
J62.0050.06; Z13.19803

[3] Polinomi e numeri di Bernoulli e di Eulero parametrizzati, Matematiche (Catania), 22 (1967), no. 1, 68-91.
Z154.06503; M36#441; R1967,12V284

[4] L'operatore xD e i numeri di Bernoulli e di Eulero, Matematiche (Catania), 31 (1976), no. 1, 63-89 (1977). (English summary).
Z381.05001; M58#10709; R1978,11B50

[5] Some results for generalized Bernoulli, Euler, Stirling numbers, Fibonacci Quart., 16 (1978), no. 2, 103-112.
Z377.10009; M58#5257; R1978,11V633

[6] Recurring sequences and Bernoulli-Euler polynomials, J. Comb. Inform. System Sci., 4 (1979), no. 4, 303-308.
Z434.10011; M81e:10010; R1981,6V560

TOSCANO L.: see also ROSSI F.S., TOSCANO L.

TOUCHARD J.,
[1] Nombres exponentiels et nombres de Bernoulli, Canad. J. Math., 8 (1956), 305-320.
Z71.06105; M18-16f; R1957,6835

[2] Sur les nombres et les polynômes de Bernoulli, Rend. del Circ. Mat. di Palermo, 50, 375-384.
J52.0355.01; TOYOIZUMI M.,
[1] Formulae for the Riemann zeta function at half integers. Tokyo J. Math. 3 (1980), no. 1, 177-186.
Z436.10018; M81j:10060

[2] Formulae for the values of zeta and $L$-functions at half integers. Tokyo J. Math. 4 (1981), no. 1, 193-201.
Z466.10033; M82h:10053; R1982,2A111

[3] Ramanujan's formulae for certain Dirichlet series, Comment. Math. Univ. St. Paul., 30 (1981), 149-173.
Correction: Comment. Math. Univ. St. Paul. 31 (1982), no. 1, 87.
Z475.10033; M83c:10058, 84b:10058

TRAKHTMAN YU. A.,
[1] The divisibility of certain differences that consist of binomial coefficients, (Russian). Akad. Nauk. Armjan. SSR Dokl., 59 (1974), no. 1, 10-16.
Z306.05003; M52#13613; R1975,5A109

[2] Divisibility of differences that consist of binomial coefficients, (Russian). Investigations in number theory, 131-137, Saratov. Gos. Univ., Saratov, 1987.
Z656.10008; M90m:11032; R1987,11A90

TRICOMI F.: see also ERDÉLYI A., MAGNUS W., OBERHETTINGER F., TRICOMI F.

TRUDI N.,
[1] Memoria sullo sviluppo di alcune funzioni trancendenti e sui numeri ultra-bernoulliani, Atti Inst. Incor. Sci. Natur. Napoli, 4 (1867), 105-131.

TSABAN B.,
[1] Bernoulli numbers and the probability of a birthday surprise. Discrete Appl. Math. 127 (2003), no. 3, 657-663.
Z1022.60006; M2004b:60023

TSCHANTZ S.T.:see RATCLIFFE J.G., TSCHANTZ S.T.

TSUJI T.,
[1] Greenberg's conjecture for Dirichlet characters of order divisible by $p$. Proc. Japan Acad. Ser. A Math. Sci. 77 (2001), no. 4, 52-54.
M2002d:11130

TSUMURA H.,
[1] On a p-adic interpolation of the generalized Euler numbers and its applications, Tokyo J. Math., 10 (1987), no. 2, 281-293.
Z641.12007; M89k:11121; R1988,8A328

[2] On the values of a $q$-analogue of the $p$-adic $L$-function. Mem. Fac. Sci. Kyushu Univ. Ser. A, 44 (1990), no. 1, 49-60.
Z716.11060; M91b:11137

[3] A note on $q$-analogues of the Dirichlet series and $q$-Bernoulli numbers. J. Number Theory, 39 (1991), no. 3, 251-256.
Z735.11009; M92j:11020

[4] On a $q$-analogue of the log-$\Gamma$-function. Nagoya Math. J., 134 (1994), 57-64.
Z804.11018; M95g:33016

[5] On Demjanenko's matrix and Maillet's determinant for imaginary abelian number fields. J. Number Theory 60 (1996), no. 1, 70-79.
(See also METSÄNKYLÄ [17]: Letter to the editor.)
Z866.11063

[6] Multiple harmonic series related to multiple Euler numbers. J. Number Theory 106 (2004), no. 1, 155-168.
M2005b:40006

[7] Certain functional relations for the double harmonic series related to the double Euler numbers. J. Aust. Math. Soc. 79 (2005), no. 3, 319-333.
M2006j:11125

TSUMURA H.:see also SRIVASTAVA H.M., TSUMURA H.

TSVETKOV V.M.,
[1] $\Gamma$-extension and the co-restriction homomorphism. (Russian). Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI), 198 (1991), Voprosy Teor. Predstav. Algebr. Grupp. 2, 103-108, 113.
Z785.11053; M93e:11129; R1992,7A373

TUAN VU KIM; NGUYEN THI TINH,
[1] Expressions of Legendre polynomials through Bernoulli polynomials. Rev. Técn. Fac. Ingr. Univ. Zulia 18 (1995), no. 3, 285-290.
Z840.33003; M97f:33019

[2] Legendre, Euler and Bernoulli polynomials. C. R. Acad. Bulgare Sci. 49 (1996), no. 5, 19-21.
Z877.33004; M98d:33004

[3] Expressions of Legendre polynomials through Euler polynomials, Math. Balkanica (N.S.) 11 (1997), no. 3-4, 295-302.
M99i:33014

TUENTER H.J.H.,
[1] On the sums $\sum_{i=1}^n\Lceil i/p \Rceil^m$ and $\sum_{i=1}^n \Lfloor i/p \Rfloor^m$}, Pi Mu Epsilon Journal 11 (2000), no. 2, 97--99.

[2] A Symmetry of Powersum Polynomials and Bernoulli numbers, Amer. Math. Monthly 108 (2001), no. 3, 258-261.
Z0983.11008; M2002e:11020

[3] The Frobenius problem, sums of powers of integers, and recurrences for the Bernoulli numbers. J. Number Theory 117 (2006), no. 2, 376--386.
M2006m:11028

TYLER D.B.,
[1] Infinite integrals that are polynomials in $\pi^2$ (Problem E 3168; solution by C. Georghiou), Amer. Math. Monthly, 96 (1989), 58-59.


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