Comptes Rendus
Number Theory
Formal groups, Bernoulli-type polynomials and L-series
Comptes Rendus. Mathématique, Volume 345 (2007) no. 6, pp. 303-306.

A new construction relating formal groups, a class of Appell polynomials called the universal Bernoulli polynomials and a family of Dirichlet L-series is proposed. Universal Bernoulli χ-numbers as well as generalized Riemann–Hurwitz zeta functions are introduced.

On propose une nouvelle construction qui relie les groupes formels à une classe de polynomes de Appell qu' on appelle polynômes de Bernoulli universels et à une famille de séries de Dirichlet. On introduit aussi les nombres de Bernoulli universels liés à un caractère de Dirichlet χ et une généralisation des fonctions de Riemann–Hurwitz.

Published online:
DOI: 10.1016/j.crma.2007.05.016

Piergiulio Tempesta 1

1 Scuola Normale Superiore, Centro di ricerca matematica Ennio de Giorgi, Piazza dei Cavalieri, 3, 56126 Pisa, Italy
     author = {Piergiulio Tempesta},
     title = {Formal groups, {Bernoulli-type} polynomials and {L-series}},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {303--306},
     publisher = {Elsevier},
     volume = {345},
     number = {6},
     year = {2007},
     doi = {10.1016/j.crma.2007.05.016},
     language = {en},
AU  - Piergiulio Tempesta
TI  - Formal groups, Bernoulli-type polynomials and L-series
JO  - Comptes Rendus. Mathématique
PY  - 2007
SP  - 303
EP  - 306
VL  - 345
IS  - 6
PB  - Elsevier
DO  - 10.1016/j.crma.2007.05.016
LA  - en
ID  - CRMATH_2007__345_6_303_0
ER  - 
%0 Journal Article
%A Piergiulio Tempesta
%T Formal groups, Bernoulli-type polynomials and L-series
%J Comptes Rendus. Mathématique
%D 2007
%P 303-306
%V 345
%N 6
%I Elsevier
%R 10.1016/j.crma.2007.05.016
%G en
%F CRMATH_2007__345_6_303_0
Piergiulio Tempesta. Formal groups, Bernoulli-type polynomials and L-series. Comptes Rendus. Mathématique, Volume 345 (2007) no. 6, pp. 303-306. doi : 10.1016/j.crma.2007.05.016.

[1] A. Adelberg Universal higher order Bernoulli numbers and Kummer and related congruences, J. Number Theory, Volume 84 (2000), pp. 119-135

[2] V.M. Bukhshtaber; A.S. Mishchenko; S.P. Novikov Formal groups and their role in the apparatus of algebraic topology, Uspekhi Mat. Nauk, Volume 26 (1971) no. 2, p. 161

[3] A. Baker Combinatorial and arithmetic identities based on formal group laws, Lecture Notes in Math., vol. 1298, Springer, 1987, pp. 17-34

[4] F. Clarke The universal von Staudt theorems, Trans. Amer. Math. Soc., Volume 315 (1989), pp. 591-603

[5] M. Hazewinkel Formal Groups and Applications, Academic Press, 1978

[6] N. Ray Stirling and Bernoulli numbers for complex oriented homology theory (G. Carlsson; R.L. Cohen; H.R. Miller; D.C. Ravenel, eds.), Algebraic Topology, Lecture Notes in Math., vol. 1370, Springer-Verlag, 1986, pp. 362-373

[7] G.C. Rota Finite Operator Calculus, Academic Press, New York, 1975

[8] J.-P. Serre, Courbes elliptiques et groupes formels, Annuaire du Collège de France (1966), 49–58 (Oeuvres, vol. II, 71, 315–324)

[9] P. Tempesta, New Appell sequences of polynomials of Bernoulli and Euler type, J. Math. Anal. Appl. (2007), in press

Cited by Sources:

Comments - Policy