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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Computing $\psi(x)$


Authors: Marc Deléglise and Joël Rivat
Journal: Math. Comp. 67 (1998), 1691-1696
MSC (1991): Primary 11Y70, 11N56
MathSciNet review: 1474649
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Abstract: Let $\Lambda$ denote the Von Mangoldt function and $ \begin{displaystyle} \psi(x)=\sum _{n \leq x} \Lambda(n) \end{displaystyle}$. 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

DOI: http://dx.doi.org/10.1090/S0025-5718-98-00977-6
PII: S 0025-5718(98)00977-6
Received by editor(s): January 23, 1997
Article copyright: © Copyright 1998 American Mathematical Society