Joint Discrete Approximation of Analytic Functions by Shifts of the Riemann Zeta-Function Twisted by Gram Points

Antanas Laurinčikas ()
Additional contact information
Antanas Laurinčikas: Institute of Mathematics, Faculty of Mathematics and Informatics, Vilnius University, Naugarduko Str. 24, LT-03225 Vilnius, Lithuania

Mathematics, 2023, vol. 11, issue 3, 1-15

Abstract: Let θ ( t ) denote the increment of the argument of the product π − s / 2 Γ ( s / 2 ) along the segment connecting the points s = 1 / 2 and s = 1 / 2 + i t , and t n denote the solution of the equation θ ( t ) = ( n − 1 ) π , n = 0 , 1 , … . The numbers t n are called the Gram points. In this paper, we consider the approximation of a collection of analytic functions by shifts in the Riemann zeta-function ( ζ ( s + i t k α 1 ) , … , ζ ( s + i t k α r ) ) , k = 0 , 1 , … , where α 1 , … , α r are different positive numbers not exceeding 1. We prove that the set of such shifts approximating a given collection of analytic functions has a positive lower density. For the proof, a discrete limit theorem on weak convergence of probability measures in the space of analytic functions is applied.

Keywords: Gram points; joint universality; weak convergence (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/11/3/565/pdf (application/pdf)
https://www.mdpi.com/2227-7390/11/3/565/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:11:y:2023:i:3:p:565-:d:1043100

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().