A converse theorem for Dirichlet L-functions

A Converse Theorem for Double Dirichlet Series and Shintani Zeta Functions Nikolaos Diamantis and Dorian Goldfeld

A Converse Theorem for Double Dirichlet Series and Shintani Zeta Functions Nikolaos Diamantis and Dorian Goldfeld

A Converse Theorem for Double Dirichlet Series and Shintani Zeta Functions

The main aim of this paper is to obtain a converse theorem for double Dirichlet series and use it to show that the Shintani zeta functions [13] which arise in the theory of prehomogeneous vector spaces are actually linear combinations of Mellin transforms of metaplectic Eisenstein series on GL(2). The converse theorem we prove will apply to a very general family of double Dirichlet series which...

A CONVERSE THEOREM FOR DOUBLE DIRICHLET SERIES By NIKOLAOS DIAMANTIS and DORIAN GOLDFELD

We prove that a certain vector valued double Dirichlet series satisfying appropriate functional equations is a Mellin transform of a vector valued metaplectic Eisenstein series. We establish an analogous result for scalar double Dirichlet series of the type studied by Siegel.

Calculation of Dirichlet L-Functions

A method for calculating Dirichlet L-series is presented along with the theory of residue class characters and their automatic generation. Tables are given of zeros of Lseries for moduli S 24.