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2010 Computing the Mertens and Meissel–Mertens Constants for Sums over Arithmetic Progressions
Alessandro Languasco, Alessandro Zaccagnini
Experiment. Math. 19(3): 279-284 (2010).

Abstract

We give explicit numerical values with 100 decimal digits for the Mertens constant involved in the asymptotic formula for $\sum_{\substack{p\le x\\ p\equiv a \operatorname{mod} q}} 1/p$ and, as a byproduct, for the Meissel-Mertens constant defined as $\sum_{p\equiv a \operatorname{mod}q} (\log(1-1/p) + 1/p)$, for $q \in \{3,\dots,100\}$ and $(q, a) = 1$. The complete set of results is available online (http://www.math.unipd.it/~languasc/Mertens-comput.html).

Citation

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Alessandro Languasco. Alessandro Zaccagnini. "Computing the Mertens and Meissel–Mertens Constants for Sums over Arithmetic Progressions." Experiment. Math. 19 (3) 279 - 284, 2010.

Information

Published: 2010
First available in Project Euclid: 4 October 2011

zbMATH: 1292.11140
MathSciNet: MR2743571

Keywords: arithmetic progressions , Mertens constants , Mertens-Meissel constants

Rights: Copyright © 2010 A K Peters, Ltd.

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Vol.19 • No. 3 • 2010
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