# On M\"untz-type formulas related to the Riemann zeta function

## TL;DR

This paper derives new M"untz-type formulas involving the Riemann zeta function using Mellin transforms and Dirichlet series, providing integral representations in critical and half-plane regions.

## Contribution

It introduces novel identities related to the Riemann zeta function in the critical strip and half-plane, expanding the analytical tools available for studying zeta-related functions.

## Key findings

- Derived M"untz-type formulas in the critical strip and Re(s)<0
- Provided integral representations for gamma and zeta function products
- Extended classical formulas to new regions of the complex plane

## Abstract

The Mellin transform and several Dirichlet series related with the Riemann zeta function are used to deduce some identities similar to the classical M\"untz formula [4]. These formulas are derived in the critical strip and in the half-plane $Re(s)<0$. As particular cases, integral representations for products of the gamma and zeta functions are exhibited.