Takashi Taniguchi

Affiliation: Kobe University, Japan

Email: tani@math.kobe-u.ac.jp

Title Of Talk: Relations among Dirichlet series whose coefficients are class numbers of binary cubic forms

Abstract: We study relations among Dirichlet series whose coefficients are class numbers of binary cubic forms in SL_2(Z)-invariant lattices. We show that each of the Dirichlet series associated with the lattices satisfies a simple explicit relation to that of the dual lattices. These series are examples of zeta functions of prehomogeneous vector spaces and satisfy certain functional equations. As an application of our result, we rewrite the functional equation in a self dual form. This is a joint work with Y. Ohno and S. Wakatsuki.

Last update made Mon May 11 14:33:07 EDT 2009.
Please report problems to: fgarvan@math.ufl.edu