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 Mosc. Math. J., 2018, Volume 18, Number 2, Pages 349–366 (Mi mmj675)

Joint value distribution theorems for the Riemann and Hurwitz zeta-functions

Antanas Laurinčikas

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

Abstract: In the paper, a class of functions $\varphi(t)$ is introduced such that a given pair of analytic functions is approximated simultaneously by shifts $\zeta(s+i\varphi(k)),\zeta(s+i\varphi(k),\alpha)$, $k\in\mathbb N$, of the Riemann and Hurwitz zeta-functions with parameter $\alpha$ for which the set $\{(\log p\colon p is prime), (\log(m+\alpha)\colon m\in\mathbb N_0)\}$ is linearly independent over $\mathbb Q$. The definition of this class includes an estimate for $\varphi(t)$ and $\varphi'(t)$ as well as uniform distribution modulo 1 of the sequence $\{a\varphi(k)\colon k\in\mathbb N\}$, $a\neq0$.

Key words and phrases: Hurwitz zeta-function, Riemann zeta-function, uniform distribution modulo 1, universality, weak convergence.

Full text: http://www.mathjournals.org/.../2018-018-002-006.html
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Document Type: Article
MSC: 11M06, 11M35
Language: English

Citation: Antanas Laurinčikas, “Joint value distribution theorems for the Riemann and Hurwitz zeta-functions”, Mosc. Math. J., 18:2 (2018), 349–366

Citation in format AMSBIB
\Bibitem{Lau18} \by Antanas~Laurin{\v{c}}ikas \paper Joint value distribution theorems for the Riemann and Hurwitz zeta-functions \jour Mosc. Math.~J. \yr 2018 \vol 18 \issue 2 \pages 349--366 \mathnet{http://mi.mathnet.ru/mmj675}