# Sharp upper bounds for fractional moments of the Riemann zeta function

## TL;DR

This paper derives precise upper bounds for the fractional moments of the Riemann zeta function on the critical line for all real exponents between 0 and 2, advancing previous results in the field.

## Contribution

It provides sharp upper bounds for the $2k$th moment of the Riemann zeta function for all real $k$ in [0,2], improving earlier bounds by Ramachandra, Heath-Brown, and Bettin-Chandee-Radziwi extlangle.

## Key findings

- Established sharp upper bounds for fractional moments of zeta on the critical line.
- Extended bounds to all real $k$ in [0,2], filling a gap in the literature.
- Improved upon previous bounds by notable researchers in the field.

## Abstract

We establish sharp upper bounds for the $2k$th moment of the Riemann zeta function on the critical line, for all real $0 \leqslant k \leqslant 2$. This improves on earlier work of Ramachandra, Heath-Brown and Bettin-Chandee-Radziwi\l\l