Approximation by generalized shifts of the Riemann zeta-function in short intervals

Abstract

It is known that the Riemann zeta-function $$\zeta (s)$$ is universal in the sense that the shifts $$\zeta (s+i\tau )$$ , $$\tau \in \mathbb {R}$$ , approximate a wide class of analytic functions. In the paper, the approximation by generalized shifts $$\zeta (s+i\varphi (\tau ))$$ , where $$\varphi (\tau )$$ is a certain differentiable function, is considered, and the property of the density for the above shifts in short intervals is obtained.