Shifted moments of the Riemann zeta function

TL;DR

This paper proves that the Riemann hypothesis implies Chandee's conjecture on shifted moments of the zeta function, using Harper's methods for bounding moments on the critical line.

Contribution

It establishes a conditional link between the Riemann hypothesis and a specific conjecture on shifted moments, advancing understanding of the zeta function's behavior.

Findings

Riemann hypothesis implies Chandee's conjecture

Uses Harper's techniques for moment bounds

Provides conditional results on shifted moments

Abstract

In this article, we prove that the Riemann hypothesis implies a conjecture of Chandee on shifted moments of the Riemann zeta function. The proof is based on ideas of Harper concerning sharp upper bounds for the $2k$-th moments of the Riemann zeta function on the critical line.