A generalization of the reciprocity law of multiple Dedekind sums
Annales de l'Institut Fourier, Volume 57 (2007) no. 2, pp. 361-377.

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.

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.

DOI: 10.5802/aif.2261
Classification: 11A15, 11B68, 11F20, 11F23, 11F50
Keywords: Dedekind sums, reciprocity law, Jacobi forms
Mot clés : somme de Dedekind, loi de reciprocité, formes de Jacobi
Asano, Masahiro 1

1 Nagoya University Graduate School of Mathemactics Chikusa-ku, Nagoya 464-8602 (Japan)
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Asano, Masahiro. A generalization of the reciprocity law of multiple Dedekind sums. Annales de l'Institut Fourier, Volume 57 (2007) no. 2, pp. 361-377. doi : 10.5802/aif.2261. https://aif.centre-mersenne.org/articles/10.5802/aif.2261/

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