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Formal groups, Bernoulli-type polynomials and \(L\)-series. (English) Zbl 1163.11063

Summary: 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 \(\chi\)-numbers as well as generalized Riemann-Hurwitz zeta functions are introduced.

MSC:

11M41 Other Dirichlet series and zeta functions
11B68 Bernoulli and Euler numbers and polynomials
14L30 Group actions on varieties or schemes (quotients)
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References:

[1] Adelberg, A., Universal higher order Bernoulli numbers and Kummer and related congruences, J. Number Theory, 84, 119-135 (2000) · Zbl 0971.11004
[2] Bukhshtaber, V. M.; Mishchenko, A. S.; Novikov, S. P., Formal groups and their role in the apparatus of algebraic topology, Uspekhi Mat. Nauk, 26, 2, 161 (1971) · Zbl 0224.57006
[3] Baker, A., Combinatorial and arithmetic identities based on formal group laws, (Lecture Notes in Math., vol. 1298 (1987), Springer), 17-34
[4] Clarke, F., The universal von Staudt theorems, Trans. Amer. Math. Soc., 315, 591-603 (1989) · Zbl 0683.10013
[5] Hazewinkel, M., Formal Groups and Applications (1978), Academic Press · Zbl 0454.14020
[6] Ray, N., Stirling and Bernoulli numbers for complex oriented homology theory, (Carlsson, G.; Cohen, R. L.; Miller, H. R.; Ravenel, D. C., Algebraic Topology. Algebraic Topology, Lecture Notes in Math., vol. 1370 (1986), Springer-Verlag), 362-373
[7] Rota, G. C., Finite Operator Calculus (1975), Academic Press: Academic Press New York
[8] J.-P. Serre, Courbes elliptiques et groupes formels, Annuaire du Collège de France (1966), 49-58 (Oeuvres, vol. II, 71, 315-324); 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; P. Tempesta, New Appell sequences of polynomials of Bernoulli and Euler type, J. Math. Anal. Appl. (2007), in press · Zbl 1176.11007
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