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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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Isolating some non-trivial zeros of zeta
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by David J. Platt PDF
Math. Comp. 86 (2017), 2449-2467 Request permission

Abstract:

We describe a rigorous algorithm to compute Riemann’s zeta function on the half line and its use to isolate the non-trivial zeros of zeta with imaginary part $\leq 30,610,046,000$ to an absolute precision of $\pm 2^{-102}$. In the process, we provide an independent verification of the Riemann Hypothesis to this height.
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Additional Information
  • David J. Platt
  • Affiliation: Heilbronn Institute for Mathematical Research, University of Bristol, University Walk, Bristol BS8 1TW, United Kingdom
  • MR Author ID: 1045993
  • Email: dave.platt@bris.ac.uk
  • Received by editor(s): March 17, 2015
  • Received by editor(s) in revised form: March 29, 2016
  • Published electronically: February 13, 2017
  • © Copyright 2017 American Mathematical Society
  • Journal: Math. Comp. 86 (2017), 2449-2467
  • MSC (2010): Primary 11Y35, 11M26
  • DOI: https://doi.org/10.1090/mcom/3198
  • MathSciNet review: 3647966