Upper bounds for fractional joint moments of the Riemann zeta function

Abstract

We establish upper bounds for the joint moments of the $2k^{\text{th}}$ power of the Riemann zeta function with the $2h^{\text{th}}$ power of its derivative for $0\le h\le 1$ and $1\le k\le 2$. These bounds are expected to be sharp based upon predictions from random matrix theory.

10 pages