Joint value-distribution of shifts of the Riemann zeta-function

Abstract

We prove that any non-zero complex values $z_1,\dots ,z_n$ can be approximated by the following integral shifts of the Riemann zeta-function $\zeta (s+i{d}_1\tau ),\dots ,\zeta (s+i{d}_n\tau )$ for infinitely many $\tau$, provided $d_1,\dots ,d_n\in \mathbb{N}$ and $s$ is a fixed complex number lying in the right open half of the critical strip.

12 pages