# Values at non-positive integers of partially twisted multiple zeta-functions I

## TL;DR

This paper investigates the values of partially twisted multiple zeta-functions at non-positive integers, providing explicit formulas using Mellin-Barnes integrals and extending previous work on fully twisted cases.

## Contribution

It introduces new explicit formulas for special values of partially twisted multiple zeta-functions at non-positive integers, building on de Crisenoy's results and Mellin-Barnes techniques.

## Key findings

- Derived explicit formulas for special values at non-positive integers.
- Extended understanding of twisted multiple zeta-functions.
- Connected fully twisted and partially twisted cases.

## Abstract

We study the behavior of partially twisted multiple zeta-functions. We give new closed and explicit formulas for special values at non-positive integer points of such zeta-functions. Our method is based on a result of M. de Crisenoy on the fully twisted case and the Mellin-Barnes integral formula.