Joint universality and generalized strong recurrence with rational parameter

JOURNAL OF NUMBER THEORY

卷:163

Article

Pankowski, Lukasz^1,2 

[1] Adam Mickiewicz Univ, Fac Math & Comp Sci, Umultowska 87, PL-61614 Poznan, Poland

[2] Nagoya Univ, Grad Sch Math, Nagoya, Aichi 4648602, Japan

关键词: Strong recurrence;    Self-approximation;    Riemann zeta function;    Riemann hypothesis;   

DOI  :  10.1016/j.jnt.2015.11.005

来源: Elsevier

【 摘 要 】

We prove that, for every rational d not equal 0, +/- 1 and every compact set K subset of {s is an element of C : 1/2 < Re(s) < 1} with connected complement, any analytic non-vanishing functions f(1), f(2) on K can be approximated, uniformly on K, by the shifts zeta(s + i tau) and zeta(s + id tau), respectively. As a consequence we deduce that the set of tau satisfying vertical bar zeta(s + i tau) - zeta (s + id tau)vertical bar < epsilon uniformly on K has a positive lower density for every d not equal 0. (c) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free