JOINT APPROXIMATION OF ANALYTIC FUNCTIONS BY SHIFTS OF THE RIEMANN AND PERIODIC HURWITZ ZETA-FUNCTIONS

Applicable Analysis and Discrete Mathematics

article

Antanas Laurincikas¹  Renata Macaitiene² 

[1] Institute of Mathematics, Faculty of Mathematics and Informatics, Vilnius University. Naugarduko str. 24;Research Institute, Siauliai University. ˇ P. Viˇsinskio str. 25

关键词: Haar measure;    Mergelyan theorem;    Riemann zeta-function;    periodic Hurwitz zeta-function;    universality.;   

DOI  :  10.2298/AADM170713016L

学科分类：社会科学、人文和艺术（综合）

来源: Univerzitet u Beogradu * Elektrotehnicki Fakultet / University of Belgrade, Faculty of Electrical Engineering

【 摘 要 】

We present some new results on the simultaneous approximation with givenaccuracy, uniformly on compact subsets of the critical strip, of a collectionof analytic functions by discrete shifts of the Riemann and periodic Hurwitzzeta-functions. We prove that the set of such shifts has a positive lowerdensity. For this, we apply the linear independence over the field of rationalnumbers of certain sets related to the zeta-functions.

【 授权许可】

Unknown