On a Generalization of Voronin's Theorem

A. Laurinčikas

Matematičeskie zametki, Tome 107 (2020) no. 3, pp. 400-411

Résumé

Voronin's theorem states that the Riemann zeta-function $\zeta(s)$ is universal in the sense that all analytic functions that are defined and have no zeros on the right half of the critical strip can be approximated by the shifts $\zeta(s+i\tau)$, $\tau \in \mathbb{R}$. Some results on the approximation by the shifts $\zeta(s+i\varphi(\tau))$ with some function $\varphi(\tau)$ are also known. In this paper, it is established that an analytic function without zeros in the strip $1/2+1/(2\alpha)\operatorname{Re} s1$ can be approximated by the shifts $\zeta(s+i\log^\alpha \tau)$ with $\alpha >1$.

Détail

Keywords: Riemann zeta-function, limit theorem, Voronin's theorem, universality.