The properties of the universal Bernoulli polynomials are illustrated and a new class of related L-functions is constructed. A generalization of the Riemann-Hurwitz zeta function is also proposed.
@article{ASNSP_2010_5_9_1_133_0, author = {Tempesta, Piergiulio}, title = {L-series and {Hurwitz} zeta functions associated with the universal formal group}, journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze}, pages = {133--144}, publisher = {Scuola Normale Superiore, Pisa}, volume = {Ser. 5, 9}, number = {1}, year = {2010}, mrnumber = {2668876}, zbl = {1203.11063}, language = {en}, url = {http://archive.numdam.org/item/ASNSP_2010_5_9_1_133_0/} }
TY - JOUR AU - Tempesta, Piergiulio TI - L-series and Hurwitz zeta functions associated with the universal formal group JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2010 SP - 133 EP - 144 VL - 9 IS - 1 PB - Scuola Normale Superiore, Pisa UR - http://archive.numdam.org/item/ASNSP_2010_5_9_1_133_0/ LA - en ID - ASNSP_2010_5_9_1_133_0 ER -
%0 Journal Article %A Tempesta, Piergiulio %T L-series and Hurwitz zeta functions associated with the universal formal group %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2010 %P 133-144 %V 9 %N 1 %I Scuola Normale Superiore, Pisa %U http://archive.numdam.org/item/ASNSP_2010_5_9_1_133_0/ %G en %F ASNSP_2010_5_9_1_133_0
Tempesta, Piergiulio. L-series and Hurwitz zeta functions associated with the universal formal group. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 9 (2010) no. 1, pp. 133-144. http://archive.numdam.org/item/ASNSP_2010_5_9_1_133_0/
[1] Universal higher order Bernoulli numbers and Kummer and related congruences, J. Number Theory 84 (2000), 119–135. | MR | Zbl
,[2] Values of Bernoulli polynomials and Hurwitz’s zeta function at rational points, C. R. Math. Acad. Sci. Soc. R. Can. 13 (1991), 104–108. | MR | Zbl
and ,[3] “Combinatorial and Arithmetic Identities Based on Formal Group Laws”, Lecture Notes in Math., Vol. 1298, Springer, 1987, 17–34. | MR
,[4] On the Kummer congruences and the stable homotopy of BU, Trans. Amer. Math. Soc. 316 (1989), 385–432. | MR | Zbl
, , and ,[5] Formal groups and their role in the apparatus of algebraic topology, Uspehi Mat. Nauk 26 (1971), 161–154. | MR | Zbl
, and ,[6] On the von Staudt-Clausen theorem, C. R. Math. Acad. Sci. Soc. R. Can. 15 (1993), 46–48. | MR | Zbl
and ,[7] “La fonction zêta”, Éditions de l’École polytechnique, 2003. | MR
and (ets.) ,[8] New formulae for the Bernoulli and Euler polynomials at rational arguments, Proc. Amer. Math. Soc. 123 (1995), 1527–1535. | MR | Zbl
and ,[9] The universal Von Staudt theorems, Trans. Amer. Math. Soc. 315 (1989), 591–603. | MR | Zbl
,[10] “History of the Theory of Numbers”, Chelsea Publishing Company, 1971.
,[11] Twisted vertex operators and Bernoulli polynomials, arXiv: math. QA/0311151 (2003). | MR | Zbl
, and ,[12] Bernoulli number identities from quantum field theory, arXiv: math. NT/0406610 (2004).
and ,[13] Faulhaber and Bernoulli polynomials and solitons, Physica D 152-153 (2001), 47–50. | MR | Zbl
and ,[14] Hodge integrals and Gromov-Witten theory, Invent. Math. 139 (2000), 173–199. | MR | Zbl
and ,[15] “Formal Groups and Applications”, Academic Press, New York, 1978. | MR | Zbl
,[16] Formal groups and zeta-functions, Osaka J. Math. 5 (1968), 199–213. | MR | Zbl
,[17] “A Classical Introduction to Modern Number Theory”, Springer-Verlag, 1982. | MR | Zbl
and ,[18] “Lectures on -adic L-Functions”, Princeton University Press, Princeton, 1972. | MR | Zbl
,[19] Polylogarithms, hyperfunctions and generalized Lipschitz summation formulae, Preprint Scuola Normale Superiore, Centro di Ricerca Matematica “Ennio De Giorgi” 1–2007, arXiv: 0712.1046v1 [math/NT] (2007). | Zbl
and ,[20] On the relation between formal groups, In: “Appell Polynomials and Hyperfunctions, Symmetry and Perturbation Theory”, G. Gaeta, R. Vitolo and S. Walcher (eds.), World Scientific, 2007, 132–139. | MR | Zbl
and ,[21] The methods of algebraic topology from the point of view of cobordism theory, Izv. Akad. Nauk SSSR Ser. Mat. 31 (1967), 885–951, transl. Math. SSR–Izv. 1 (1967), 827–913. | MR
,[22] “Modular Forms and Dirichlet Series”, Mathematics Lecture Note Series, W. A. Benjamin, Inc., 1969. | MR | Zbl
,[23] Stirling and Bernoulli numbers for complex oriented homology theory, In: “Algebraic Topology”, G. Carlsson, R. L. Cohen, H. R. Miller and D. C. Ravenel (eds.), Lecture Notes in Math., Vol. 1370, Springer-Verlag, 1986, 362–373, | Zbl
,[24] “Finite Operator Calculus”, Academic Press, New York, 1975.
,[25] Courbes elliptiques et groupes formels, Annuaire du Collège de France (1966), 49–58. (Oeuvres, Vol. II, 71, 315–324.)
,[26] Bernoulli-type polynomials and L-series, C. R. Math. Acad. Sci. Paris, Ser. I 345 (2007), 303–306. | MR
, ,[27] On new Appell sequences of polynomials of Bernoulli and Euler type, J. Math. Anal. Appl. 341 (2008), 1295–1310. | MR | Zbl
,[28] Congruence for Bernoulli, Euler and Stirling Numbers, J. Number Theory 78 (1999), 204–227. | MR
,