Zeta invariants for Dirichlet series

Multiple Dirichlet Series and Moments of Zeta and L–functions

This paper develops an analytic theory of Dirichlet series in several complex variables which possess sufficiently many functional equations. In the first two sections it is shown how straightforward conjectures about the meromorphic continuation and polar divisors of certain such series imply, as a consequence, precise asymptotics (previously conjectured via random matrix theory) for moments o...

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...

Dirichlet Series

This definition could have been given to an 18th or early 19th century mathematical audience, but it would not have been very popular: probably they would not have been comfortable with the Humpty Dumpty-esque redefinition of multiplication. Mathematics at that time did have commutative rings: rings of numbers, of matrices, of functions, but not rings with a “funny” multiplication operation def...