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Mosc. Math. J., 2015, Volume 15, Number 2, Pages 283–291 (Mi mmj559)  

A note on Artin's constant

Ivan Cherednik

Department of Mathematics, UNC Chapel Hill, North Carolina 27599, USA

Abstract: We suggest new heuristic summation formulas for the Artin constant and its analogs in higher ranks, for the density of prime numbers $p$ such that a given set of integers generates the corresponding multiplicative groups modulo powers of $p$. Depending on the choice of these integers, certain interesting rational corrections emerge, which are calculated in rank one case. The rate of convergence of these sums to the corresponding constants, connected with the generalized Riemann Hypothesis, is analyzed numerically. We also discuss the Stephens constant.

Key words and phrases: Artin constant, Riemann hypothesis.

DOI: https://doi.org/10.17323/1609-4514-2015-15-2-283-291

Full text: http://www.mathjournals.org/.../2015-015-002-006.html
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Bibliographic databases:

MSC: 11M06, 11N69, 11Z05
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Citation: Ivan Cherednik, “A note on Artin's constant”, Mosc. Math. J., 15:2 (2015), 283–291

Citation in format AMSBIB
\Bibitem{Che15}
\by Ivan~Cherednik
\paper A note on Artin's constant
\jour Mosc. Math.~J.
\yr 2015
\vol 15
\issue 2
\pages 283--291
\mathnet{http://mi.mathnet.ru/mmj559}
\crossref{https://doi.org/10.17323/1609-4514-2015-15-2-283-291}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3427424}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000361607300006}


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