An Elliptic Analogue Of Generalized Cotangent Dirichlet Series And Its Transformation Formulae At Some Integer Arguments

Details An Elliptic Analogue Of Generalized Cotangent Dirichlet Series And Its Transformation Formulae At Some Integer Arguments An Elliptic Analogue Of Generalized Cotangent Dirichlet Series And Its Transformation Formulae At Some Integer Arguments

2011-07-25

arxiv.org/abs/1107.4933v1

Mathematics

Number Theory

34pages

Scientific paper

B.C. Berndt evaluated special values of the cotangent Dirichlet series. T. Arakawa studied a generalization of the series, or generalized cotangent Dirichlet series, and gave its transformation formulae. In this paper, we establish an elliptic analogue of the generalized cotangent Dirichlet series and give its transformation formulae at some integer arguments. As a corollary, we obtain the transformation formulae of the generalized cotangent Dirichlet series at some integer arguments which are the part of Arakawa's transformation formulae. Those transformation formulae give the special values of the cotangent Dirichlet series evaluated by B.C. Berndt.

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