A generalization of the reciprocity law of multiple Dedekind sums

Masahiro Asano[1]

  • [1] Nagoya University Graduate School of Mathemactics Chikusa-ku, Nagoya 464-8602 (Japan)

Annales de l’institut Fourier (2007)

  • Volume: 57, Issue: 2, page 361-377
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Asano, Masahiro. "A generalization of the reciprocity law of multiple Dedekind sums." Annales de l’institut Fourier 57.2 (2007): 361-377. <http://eudml.org/doc/10225>.

@article{Asano2007,
abstract = {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.},
affiliation = {Nagoya University Graduate School of Mathemactics Chikusa-ku, Nagoya 464-8602 (Japan)},
author = {Asano, Masahiro},
journal = {Annales de l’institut Fourier},
keywords = {Dedekind sums; reciprocity law; Jacobi forms},
language = {eng},
number = {2},
pages = {361-377},
publisher = {Association des Annales de l’institut Fourier},
title = {A generalization of the reciprocity law of multiple Dedekind sums},
url = {http://eudml.org/doc/10225},
volume = {57},
year = {2007},
}

TY - JOUR
AU - Asano, Masahiro
TI - A generalization of the reciprocity law of multiple Dedekind sums
JO - Annales de l’institut Fourier
PY - 2007
PB - Association des Annales de l’institut Fourier
VL - 57
IS - 2
SP - 361
EP - 377
AB - 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.
LA - eng
KW - Dedekind sums; reciprocity law; Jacobi forms
UR - http://eudml.org/doc/10225
ER -

References

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