Approximation by special values of Dirichlet series

Çam Çelik, Şermin; Göral, Haydar

doi:10.1090/proc/14715

Approximation by special values of Dirichlet series
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by Şermin Çam Çelik and Haydar Göral PDF

Proc. Amer. Math. Soc. 148 (2020), 83-93 Request permission

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 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.

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