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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.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Estimating $\pi (x)$ and related functions under partial RH assumptions
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by Jan Büthe PDF
Math. Comp. 85 (2016), 2483-2498 Request permission


We give a direct interpretation of the validity of the Riemann hypothesis for all zeros with $\Im (\rho )\in (0,T]$ in terms of the prime-counting function $\pi (x)$ by proving that Schoenfeld’s explicit estimates for $\pi (x)$ and the Chebyshov functions hold as long as $4.92\sqrt {x/\log (x)} \leq T$.

We also improve some of the existing bounds of Chebyshov type for the function $\psi (x)$.

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Additional Information
  • Jan Büthe
  • Affiliation: Mathematisches Institut, Endenicher Allee 60, 53115 Bonn, Germany
  • MR Author ID: 1017601
  • Email:
  • Received by editor(s): November 13, 2014
  • Received by editor(s) in revised form: March 11, 2015, and March 15, 2015
  • Published electronically: December 1, 2015
  • © Copyright 2015 American Mathematical Society
  • Journal: Math. Comp. 85 (2016), 2483-2498
  • MSC (2010): Primary 11N05; Secondary 11M26
  • DOI:
  • MathSciNet review: 3511289