[Une généralisation de la loi de reciprocité des sommes multiples de Dedekind]
Plusieurs sommes multiples de Dedekind ont été introduites par B.C.Berndt, L.Carlitz, S.Egami, D.Zagier et A.Bayad. Dans cet article, après avoir remarqué la forme de Jacobi dans Bayad [4], la fonction cotangente dans Zagier [23], le résultat d’Egami sur les fonctions cotangentes [14] et leurs lois de reciprocité, nous étudions un cas spécial de la forme de Jacobi de Bayad [4] et déduisons une généralisation du résultat d’Egami sur les fonctions cotangentes et une généralisation du résultat de Zagier. De plus, nous considérons leurs lois de réciprocité.
Various multiple Dedekind sums were introduced by B.C.Berndt, L.Carlitz, S.Egami, D.Zagier and A.Bayad.
In this paper, noticing the Jacobi form in Bayad [4], the cotangent function in Zagier [23], Egami’s result on cotangent functions [14] and their reciprocity laws, we study a special case of the Jacobi forms in Bayad [4] and deduce a generalization of Egami’s result on cotangent functions and a generalization of Zagier’s result. Further, we consider their reciprocity laws.
Keywords: Dedekind sums, reciprocity law, Jacobi forms
Mot clés : somme de Dedekind, loi de reciprocité, formes de Jacobi
@article{AIF_2007__57_2_361_0,
author = {Asano, Masahiro},
title = {A generalization of the reciprocity law of multiple {Dedekind} sums},
journal = {Annales de l'Institut Fourier},
pages = {361--377},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {57},
number = {2},
year = {2007},
doi = {10.5802/aif.2261},
zbl = {1158.11022},
mrnumber = {2310944},
language = {en},
url = {http://www.numdam.org/articles/10.5802/aif.2261/}
}
TY - JOUR AU - Asano, Masahiro TI - A generalization of the reciprocity law of multiple Dedekind sums JO - Annales de l'Institut Fourier PY - 2007 SP - 361 EP - 377 VL - 57 IS - 2 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.2261/ DO - 10.5802/aif.2261 LA - en ID - AIF_2007__57_2_361_0 ER -
%0 Journal Article %A Asano, Masahiro %T A generalization of the reciprocity law of multiple Dedekind sums %J Annales de l'Institut Fourier %D 2007 %P 361-377 %V 57 %N 2 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.2261/ %R 10.5802/aif.2261 %G en %F AIF_2007__57_2_361_0
Asano, Masahiro. A generalization of the reciprocity law of multiple Dedekind sums. Annales de l'Institut Fourier, Tome 57 (2007) no. 2, pp. 361-377. doi : 10.5802/aif.2261. http://www.numdam.org/articles/10.5802/aif.2261/
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