[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.
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@article{CRMATH_2011__349_3-4_131_0,
author = {Bayad, Abdelmejid and Raouj, Abdelaziz},
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},
url = {http://www.numdam.org/articles/10.1016/j.crma.2010.12.011/}
}
TY - JOUR AU - Bayad, Abdelmejid AU - Raouj, Abdelaziz TI - Reciprocity formulae for multiple Dedekind–Rademacher sums JO - Comptes Rendus. Mathématique PY - 2011 SP - 131 EP - 136 VL - 349 IS - 3-4 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2010.12.011/ DO - 10.1016/j.crma.2010.12.011 LA - en ID - CRMATH_2011__349_3-4_131_0 ER -
%0 Journal Article %A Bayad, Abdelmejid %A Raouj, Abdelaziz %T Reciprocity formulae for multiple Dedekind–Rademacher sums %J Comptes Rendus. Mathématique %D 2011 %P 131-136 %V 349 %N 3-4 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2010.12.011/ %R 10.1016/j.crma.2010.12.011 %G en %F CRMATH_2011__349_3-4_131_0
Bayad, Abdelmejid; Raouj, Abdelaziz. Reciprocity formulae for multiple Dedekind–Rademacher sums. Comptes Rendus. Mathématique, Tome 349 (2011) no. 3-4, pp. 131-136. doi : 10.1016/j.crma.2010.12.011. http://www.numdam.org/articles/10.1016/j.crma.2010.12.011/
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