A generalization of the reciprocity law of multiple Dedekind sums
[Une généralisation de la loi de reciprocité des sommes multiples de Dedekind]
Annales de l'Institut Fourier, Tome 57 (2007) no. 2, pp. 361-377.

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.

DOI : https://doi.org/10.5802/aif.2261
Classification : 11A15,  11B68,  11F20,  11F23,  11F50
Mots 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},
     mrnumber = {2310944},
     zbl = {1158.11022},
     language = {en},
     url = {http://archive.numdam.org/articles/10.5802/aif.2261/}
}
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://archive.numdam.org/articles/10.5802/aif.2261/

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