Geodesic
On a Generalization of Voronin's Theorem
Matematičeskie zametki, Tome 107 (2020) no. 3, pp. 400-411.

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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 $\alpha >1$.
Keywords: Riemann zeta-function, limit theorem, Voronin's theorem, universality. 
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A. Laurinčikas. On a Generalization of Voronin's Theorem. Matematičeskie zametki, Tome 107 (2020) no. 3, pp. 400-411. http://geodesic.mathdoc.fr/item/MZM_2020_107_3_a6/

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