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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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Computing $\psi (x)$
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by Marc Deléglise and Joël Rivat PDF
Math. Comp. 67 (1998), 1691-1696 Request permission

Abstract:

Let $\Lambda$ denote the Von Mangoldt function and $\psi (x)=\sum _{n \leq x} \Lambda (n)$. We describe an elementary method for computing isolated values of $\psi (x)$. The complexity of the algorithm is $O(x^{2/3}(\log \log x)^{1/3})$ time and $O(x^{1/3}(\log \log x)^{2/3})$ space. A table of values of $\psi (x)$ for $x$ up to $10^{15}$ is included, and some times of computation are given.
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Additional Information
  • Marc Deléglise
  • Affiliation: Institut Girard Desargues, UPRES-A 5028 Mathematiques, Université Lyon I, 69622 Villeurbanne Cedex, France
  • Email: deleglis@desargues.univ-lyon1.fr
  • Joël Rivat
  • Affiliation: Institut Girard Desargues, UPRES-A 5028 Mathematiques, Université Lyon I, 69622 Villeurbanne Cedex, France
  • Email: rivat@desargues.univ-lyon1.fr
  • Received by editor(s): January 23, 1997
  • © Copyright 1998 American Mathematical Society
  • Journal: Math. Comp. 67 (1998), 1691-1696
  • MSC (1991): Primary 11Y70, 11N56
  • DOI: https://doi.org/10.1090/S0025-5718-98-00977-6
  • MathSciNet review: 1474649