# On some mellin transforms for the Riemann zeta function in the critical strip

## TL;DR

This paper introduces two new Mellin transform evaluations for the Riemann zeta function within the critical strip, providing insights into related Fourier integrals involving the Riemann xi function.

## Contribution

The paper presents novel Mellin transform formulas for the Riemann zeta function in the critical strip, expanding analytical tools for studying its properties.

## Key findings

- New Mellin transform evaluations for ζ(s) in 0<Re(s)<1
- Discussion on Fourier integrals involving the Riemann xi function
- Enhanced understanding of the zeta function's integral representations

## Abstract

We offer two new Mellin transform evaluations for the Riemann zeta function in the region $0<\Re(s)<1.$ Some discussion is offered in the way of evaluating some further Fourier integrals involving the Riemann xi function.