A relation between the Mordell-Tornheim multiple Dirichlet series and the confluent hypergeometric function

TL;DR

This paper explores a connection between Mordell-Tornheim multiple Dirichlet series and confluent hypergeometric functions, establishing functional equations for double L-functions using Mellin-Barnes integrals.

Contribution

It introduces a novel relation between multiple Dirichlet series and hypergeometric functions, and derives new functional equations for double L-functions.

Findings

Established a relation between Mordell-Tornheim series and hypergeometric functions.

Derived functional equations for double L-functions.

Applied Mellin-Barnes integral formula to prove main results.

Abstract

We investigate a relation between the Mordell-Tornheim type of multiple Dirichlet series and a confluent hypergeometric function. We prove it by applying the Mellin-Barnes integral formula. Also, main results in this paper contain two kinds of functional equations for double $L$-functions as a special case.