A new multiple Dirichlet series induced by a higher order form

TL;DR

This paper constructs a new two-variable multiple Dirichlet series from a higher order Eisenstein series, demonstrating its meromorphic extension and functional equations, advancing the understanding of automorphic forms and Dirichlet series.

Contribution

It introduces a novel multiple Dirichlet series associated with higher order forms, extending the theory of automorphic L-functions.

Findings

Series extends meromorphically

Satisfies two independent functional equations

Connects higher order Eisenstein series with Dirichlet series

Abstract

A multiple Dirichlet series in two variables is constructed as a Mellin transform of a higher order Eisenstein series. It is shown to extend to a meromorphic function and satisfy two independent functional equations.