Short proofs, generalizations and applications of certain identities concerning multiple Dirichlet series

TL;DR

This paper offers new proofs, generalizations, and analogues of identities related to multiple Dirichlet series, and applies these results to derive asymptotic formulas with error estimates for related sums.

Contribution

It introduces alternative proofs and broader generalizations of existing identities in multiple Dirichlet series, expanding their theoretical framework.

Findings

New proofs and generalizations of multiple Dirichlet series identities

Asymptotic formulas with remainder terms for related sums

Extended applications of Dirichlet series identities

Abstract

We present other proofs, generalizations and analogues of the identities concerning multiple Dirichlet series by Tahmi and Derbal (2022). As applications, we obtain asymptotic formulas with remainder terms for certain related sums.