Dedekind symbols associated with J-forms and their reciprocity law
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- 作者：Fukuhara ; Shinji
- 关键词：primary 11F20 ; secondary 11F67 ; 33E05 ; Dedekind sum ; Jacobi form ; Reciprocity law
- 刊名：Journal of Number Theory
- 出版年：2003
- 出版时间：February, 2003
- 年：2003
- 卷：98
- 期：2
- 页码：236-253
- 全文大小：178 K
文摘
We define a Dedekind symbol associated with a J-form (J-forms generalize the usual Jacobi forms). Then we prove the reciprocity law for Dedekind symbols. As an example, we give an explicit description for the Dedekind symbol associated with Weierstrass 
-function. The reciprocity law in this case then yields new trigonometric identities. This in turn gives rise to a “generating function” of Apostol reciprocity law for the generalized Dedekind sums.
-function. The reciprocity law in this case then yields new trigonometric identities. This in turn gives rise to a “generating function” of Apostol reciprocity law for the generalized Dedekind sums.