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Computing

Authors:	Marc Delé glise Joë l Rivat.

Affiliation:	Institut Girard Desargues, UPRES-A 5028 Mathematiques, Université Lyon I, 69622 Villeurbanne Cedex, France ; Institut Girard Desargues, UPRES-A 5028 Mathematiques, Université Lyon I, 69622 Villeurbanne Cedex, France

Abstract:	Let 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 . The complexity of the algorithm is $O(x^{2/3}(loglog x)^{1/3})$ time and $O(x^{1/3}(loglog x)^{2/3})$ space. A table of values of for up to $10^{15}$ is included, and some times of computation are given.

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