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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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A still sharper region where $\pi (x)-{\mathrm {li}}(x)$ is positive
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by Yannick Saouter, Timothy Trudgian and Patrick Demichel PDF
Math. Comp. 84 (2015), 2433-2446 Request permission

Abstract:

We consider the least number $x$ for which a change of sign of $\pi (x)-\mathrm {li}(x)$ occurs. First, we consider modifications of Lehman’s method that enable us to obtain better estimates of some error terms. Second, we establish a new smaller upper bound for the first $x$ for which the difference is positive. Third, we use numerical computations to improve the final result.
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Additional Information
  • Yannick Saouter
  • Affiliation: Institut Telecom Brest, Department Informatique, CS 83818, 29238 Brest, Cedex 3 France
  • Email: Yannick.Saouter@enst-bretagne.fr
  • Timothy Trudgian
  • Affiliation: The Australian National University, Mathematical Sciences Institute, Building 27, ACTON, ACT 0200 Australia
  • MR Author ID: 909247
  • Email: timothy.trudgian@anu.edu.au
  • Patrick Demichel
  • Affiliation: Hewlett-Packard France, 91947 Les Ulis, Cedex France
  • Email: patrick.demichel@hp.com
  • Received by editor(s): June 11, 2013
  • Received by editor(s) in revised form: December 4, 2013
  • Published electronically: February 12, 2015
  • Additional Notes: The second author was supported in part by ARC Grant DE120100173.
  • © Copyright 2015 American Mathematical Society
  • Journal: Math. Comp. 84 (2015), 2433-2446
  • MSC (2010): Primary 11-04, 11A15, 11M26, 11Y11, 11Y35
  • DOI: https://doi.org/10.1090/S0025-5718-2015-02930-5
  • MathSciNet review: 3356033