APPROXIMATION BY SPECIAL VALUES OF DIRICHLET SERIES

Celik S. C., Goral H.

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, vol.148, no.1, pp.83-93, 2020 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 148 Issue: 1
  • Publication Date: 2020
  • Doi Number: 10.1090/proc/14715
  • Journal Name: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, DIALNET
  • Page Numbers: pp.83-93
  • Keywords: Dirichlet series, approximation, arithmetic progressions, ZETA-FUNCTION
  • Dokuz Eylül University Affiliated: Yes

Abstract

In this note, we will show that real numbers can be strongly approximated by linear combinations of special values of Dirichlet series. We extend the approximation results of Emre Alkan in an effective way to all non-zero Dirichlet series with a better approximation. Using the fundamental works of Szemeredi and Green-Tao on arithmetic progressions, we prove that one can approximate real numbers with special values of Dirichlet series coming from sets of positive upper density or the set of prime numbers.