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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.78.

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Improvements to Turing’s method
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by Timothy Trudgian PDF
Math. Comp. 80 (2011), 2259-2279 Request permission


This article improves the estimate of the size of the definite integral of $S(t)$, the argument of the Riemann zeta-function. The primary application of this improvement is Turing’s Method for the Riemann zeta-function. Analogous improvements are given for the arguments of Dirichlet $L$-functions and of Dedekind zeta-functions.
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Additional Information
  • Timothy Trudgian
  • Affiliation: Mathematical Institute, University of Oxford, OX1 3LB England
  • Address at time of publication: Department of Mathematics and Computer Science, University of Lethbridge, University Drive W, Lethbridge, AB, T1K 3M4, Canada
  • MR Author ID: 909247
  • Email:
  • Received by editor(s): December 9, 2009
  • Received by editor(s) in revised form: August 2, 2010
  • Published electronically: March 1, 2011
  • Additional Notes: I wish to acknowledge the financial support of the General Sir John Monash Foundation, and Merton College, Oxford.
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Math. Comp. 80 (2011), 2259-2279
  • MSC (2010): Primary 11M06, 11R42; Secondary 11M26
  • DOI:
  • MathSciNet review: 2813359