[Lois de réciprocité pour les sommes multiples de Dedekind–Rademacher]
Nous introduisons les sommes multiples de Dedekind–Rademacher, écrites en termes de valeurs des fonctions de Bernoulli. Ses sommes généralisent les sommes classiques de Dedekind–Rademacher. Dans ce travail, nous avons établi une loi de réciprocité pour ces sommes. Notre résultat unifie et généralise tous les résultats connus sur les sommes de Dedekind–Rademacher.
We introduce multiple Dedekind–Rademacher sums, in terms of values of Bernoulli functions, that generalize the classical Dedekind–Rademacher sums. The aim of this paper is to give and prove a reciprocity law for these sums. The main theorem presented in this paper contains all previous results in the literature about Dedekind–Rademacher sums.
Accepté le :
Publié le :
Abdelmejid Bayad 1 ; Abdelaziz Raouj 2
@article{CRMATH_2011__349_3-4_131_0,
author = {Abdelmejid Bayad and Abdelaziz Raouj},
title = {Reciprocity formulae for multiple {Dedekind{\textendash}Rademacher} sums},
journal = {Comptes Rendus. Math\'ematique},
pages = {131--136},
publisher = {Elsevier},
volume = {349},
number = {3-4},
year = {2011},
doi = {10.1016/j.crma.2010.12.011},
language = {en},
}
Abdelmejid Bayad; Abdelaziz Raouj. Reciprocity formulae for multiple Dedekind–Rademacher sums. Comptes Rendus. Mathématique, Volume 349 (2011) no. 3-4, pp. 131-136. doi : 10.1016/j.crma.2010.12.011. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.12.011/
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- Reciprocity formulae for generalized Dedekind and Hardy–Berndt sums involving Apostol–Bernoulli polynomials and functions, The Ramanujan Journal, Volume 67 (2025) no. 1 | DOI:10.1007/s11139-025-01026-5
- Reciprocity formulae for generalized Dedekind–Rademacher sums attached to three Dirichlet characters and related polynomial reciprocity formulae, International Journal of Number Theory, Volume 20 (2024) no. 06, p. 1463 | DOI:10.1142/s1793042124500726
- Mean square values of L-functions over subgroups for nonprimitive characters, Dedekind sums and bounds on relative class numbers, Canadian Journal of Mathematics, Volume 75 (2023) no. 5, p. 1711 | DOI:10.4153/s0008414x2300010x
- Applications of Symmetric Identities for Apostol–Bernoulli and Apostol–Euler Functions, Symmetry, Volume 15 (2023) no. 7, p. 1384 | DOI:10.3390/sym15071384
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