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Mathematics of Computation

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Improved results on the Mertens conjecture

Authors: Yannick Saouter and Herman te Riele
Journal: Math. Comp. 83 (2014), 421-433
MSC (2010): Primary 11-04, 11A15, 11M26, 11Y11, 11Y35
Published electronically: May 28, 2013
MathSciNet review: 3120597
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Abstract: In this article, we study the Mertens conjecture. We revisit and improve the original constructive disproof of János Pintz. We obtain a new lower bound for the minimal counterexample and new numerical results for this conjecture.

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Additional Information

Yannick Saouter
Affiliation: Institut Telecom Brest, Bretagne

Herman te Riele
Affiliation: CWI, Amsterdam, Netherlands

Received by editor(s): December 14, 2011
Received by editor(s) in revised form: April 26, 2012, and May 9, 2012
Published electronically: May 28, 2013
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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