Discrete restrictions from Laurent monomial systems for multiple Dirichlet series

TL;DR

This paper introduces a special class of multiple Dirichlet series supported on algebraic varieties with Euler product structure, proposing conjectures on their analytic properties.

Contribution

It defines a new class of multiple Dirichlet series with geometric support and formulates conjectures on their analytic behavior.

Findings

Series supported on a variety with Euler product structure

Proposed conjectures on analytic properties of these series

Framework connecting algebraic geometry and Dirichlet series

Abstract

We introduce a special class of multiple Dirichlet series whose terms are supported on a variety and which admit an Euler product structure. We proposed several conjectures on the analytic properties of these series.