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

   

 

A sharp region where $ \pi(x)-{\mathrm{li}}(x)$ is positive


Authors: Yannick Saouter and Patrick Demichel
Journal: Math. Comp. 79 (2010), 2395-2405
MSC (2010): Primary 11-04, 11A41, 11M26, 11N05, 11Y11, 11Y35
Published electronically: April 14, 2010
MathSciNet review: 2684372
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Abstract | References | Similar Articles | Additional Information

Abstract: In this article, we study the problem of changes of sign of $ \pi(x)-{\mathrm{li}}(x)$. We provide three improvements. First, we give better esimates of error term for Lehman's theorem. Second, we rigorously prove the positivity of this difference for a region formerly conjectured by Patrick Demichel. Third, we improve the estimates for regions of positivity by using number theoretic results.


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Additional Information

Yannick Saouter
Affiliation: Institut Telecom Brest, Bretagne
Email: Yannick.Saouter@telecom-bretagne.eu

Patrick Demichel
Affiliation: Hewlett-Packard France, Les Ulis
Email: patrick.demichel@hp.com

DOI: http://dx.doi.org/10.1090/S0025-5718-10-02351-3
Received by editor(s): January 8, 2009
Received by editor(s) in revised form: May 4, 2009, and July 31, 2009
Published electronically: April 14, 2010
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.



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