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Proceedings of the American Mathematical Society

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Approximation by special values of Dirichlet series


Authors: Şermin Çam Çelik and Haydar Göral
Journal: Proc. Amer. Math. Soc. 148 (2020), 83-93
MSC (2010): Primary 11M41, 41A30, 42A16
DOI: https://doi.org/10.1090/proc/14715
Published electronically: July 30, 2019
MathSciNet review: 4042832
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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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Additional Information

Şermin Çam Çelik
Affiliation: Department of Natural and Mathematical Sciences, Faculty of Engineering, Özyegin University, Çekmekoy 34794, Istanbul, Turkey
Email: sermincamcelik@gmail.com

Haydar Göral
Affiliation: Department of Mathematics, Faculty of Science, Tınaztepe Campus, Dokuz Eylül University, Buca, 35160 Izmir, Turkey
Email: hgoral@gmail.com

Keywords: Dirichlet series, approximation, arithmetic progressions
Received by editor(s): May 24, 2018
Received by editor(s) in revised form: April 19, 2019
Published electronically: July 30, 2019
Communicated by: Benjamin Brubaker
Article copyright: © Copyright 2019 American Mathematical Society