Joint approximation of analytic functions by shifts of the Riemann zeta-function twisted by the Gram function

Abstract

In the paper, we consider the simultaneous approximation of a collection of analytic functions by a collection of shifts of the Riemann zeta-function $(\zeta(s+it_\tau^{\alpha_1}), \dots, \zeta(s+it_\tau^{\alpha_r}))$, where $t_\tau$ is the Gram function and $\alpha_1, \dots, \alpha_r$ are different positive numbers. It is obtained that the set of such shifts has a positive lower density.