Relations among Dirichlet series whose coefficients are class numbers of binary cubic forms II
Number Theory
2011-12-22 v1
Abstract
As a continuation of the authors and Wakatsuki's previous paper [5], we study relations among Dirichlet series whose coefficients are class numbers of binary cubic forms. We show that for any integral models of the space of binary cubic forms, the associated Dirichlet series satisfies a simple explicit relation to that of the dual other than the usual functional equation. As an application, we write the functional equations of these Dirichlet series in self dual forms.
Cite
@article{arxiv.1112.5029,
title = {Relations among Dirichlet series whose coefficients are class numbers of binary cubic forms II},
author = {Yasuo Ohno and Takashi Taniguchi},
journal= {arXiv preprint arXiv:1112.5029},
year = {2011}
}
Comments
12 pages; submitted