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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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High precision computation of Riemann’s zeta function by the Riemann-Siegel formula, I
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by J. Arias de Reyna PDF
Math. Comp. 80 (2011), 995-1009 Request permission

Abstract:

We present rigorous and sharp bounds for the terms and remainder in the Riemann-Siegel formula (for a general argument, not necessarily on the critical line). This allows for the computation of $\zeta (s)$ and $Z(t)$ to high precision. We also derive the Riemann-Siegel formula in a new and more direct way.
References
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Additional Information
  • J. Arias de Reyna
  • Affiliation: Facultad de Matemáticas, Universidad de Sevilla, Apdo. 1160, 41080-Sevilla, Spain
  • ORCID: 0000-0003-3348-4374
  • Email: arias@us.es
  • Received by editor(s): December 3, 2009
  • Received by editor(s) in revised form: February 25, 2010
  • Published electronically: September 24, 2010
  • Additional Notes: The author was supported by grant MTM2009-08934.
  • © Copyright 2010 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Math. Comp. 80 (2011), 995-1009
  • MSC (2010): Primary 11M06, 11Y35; Secondary 65E05
  • DOI: https://doi.org/10.1090/S0025-5718-2010-02426-3
  • MathSciNet review: 2772105