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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

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
Email: Yannick.Saouter@enst-bretagne.fr

Herman te Riele
Affiliation: CWI, Amsterdam, Netherlands
Email: Herman.te.Riele@cwi.nl

DOI: http://dx.doi.org/10.1090/S0025-5718-2013-02716-0
PII: S 0025-5718(2013)02716-0
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.