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SELF-APPROXIMATION FOR THE RIEMANN ZETA FUNCTION

Part of: Probabilistic theory: distribution modulo $1$; metric theory of algorithms

Published online by Cambridge University Press:  31 October 2012

TAKASHI NAKAMURA  and
ŁUKASZ PAŃKOWSKI
TAKASHI NAKAMURA
Affiliation:
Department of Mathematics, Faculty of Science and Technology, Tokyo University of Science Noda, Chiba 278-8510, Japan (email: nakamura_takashi@ma.noda.tus.ac.jp)
ŁUKASZ PAŃKOWSKI*
Affiliation:
Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Umultowska 87, 61-614 Poznań, Poland (email: lpan@amu.edu.pl)
*
✉For correspondence; e-mail: lpan@amu.edu.pl
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Abstract

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In the paper we deal with self-approximation of the Riemann zeta function in the half plane $\operatorname {Re} s\gt 1$ and in the right half of the critical strip. We also prove some results concerning joint universality and joint value approximation of functions $\zeta (s+\lambda +id\tau )$ and $\zeta (s+i\tau )$.

Keywords

hybrid universalitythe Riemann zeta functionself-approximation

MSC classification

Secondary: 11K60: Diophantine approximation
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 87 , Issue 3 , June 2013 , pp. 452 - 461
Copyright
Copyright © 2012 Australian Mathematical Publishing Association Inc. 

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