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Algebra i Analiz, 2018, Volume 30, Issue 1, Pages 139–150 (Mi aa1574)  

Research Papers

Discrete universality of the Riemann zeta-function and uniform distribution modulo 1

A. Laurinčikas

Faculty of Mathematics and Informatics, Vilnius University, Naugarduko str. 24, LT-03225 Vilnius, Lithuania

Abstract: It is proved that a wide class of analytic functions can be approximated by shifts $\zeta(s+i\varphi(k))$, $k\geqslant k_0$, $k\in\mathbb N$, of the Riemann zeta-function. Here the function $\varphi(t)$ has a continuous nonvanishing derivative on $[k_0,\infty)$ satisfying the estimate $\varphi(2t)\max_{t\leqslant u\leqslant2t}(\varphi'(u))^{-1}\ll t$, and the sequence $\{a\varphi(k)\colon k\geqslant k_0\}$ with every real $a\neq0$ is uniformly distributed modulo 1. Examples of $\varphi(t)$ are given.

Keywords: Riemann zeta-function, uniform distribution modulo 1, universality, weak convergence.

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English version:
St. Petersburg Mathematical Journal, 2019, 30:1, 103–110

Bibliographic databases:

MSC: 11M06
Received: 26.11.2016
Language:

Citation: A. Laurinčikas, “Discrete universality of the Riemann zeta-function and uniform distribution modulo 1”, Algebra i Analiz, 30:1 (2018), 139–150; St. Petersburg Math. J., 30:1 (2019), 103–110

Citation in format AMSBIB
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