APPROXIMATION BY SPECIAL VALUES OF DIRICHLET SERIES

Celik S. C., Goral H.

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, cilt.148, sa.1, ss.83-93, 2020 (SCI-Expanded, Scopus) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 148 Sayı: 1
  • Basım Tarihi: 2020
  • Doi Numarası: 10.1090/proc/14715
  • Dergi Adı: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, DIALNET
  • Sayfa Sayıları: ss.83-93
  • Anahtar Kelimeler: Dirichlet series, approximation, arithmetic progressions
  • Dokuz Eylül Üniversitesi Adresli: Evet

Özet

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.