Open AccessApproximation by special values of Dirichlet series
Author(s) -
Şermin Çam Çelik,
Haydar Göral
Publication year - 2019
Publication title -
proceedings of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.968
H-Index - 84
eISSN - 1088-6826
pISSN - 0002-9939
DOI - 10.1090/proc/14715
Subject(s) - mathematics , series (stratigraphy) , dirichlet series , general dirichlet series , dirichlet distribution , set (abstract data type) , zero (linguistics) , analytic number theory , pure mathematics , mathematical analysis , computer science , paleontology , boundary value problem , linguistics , philosophy , programming language , biology
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 Szemerédi 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.