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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.

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Note on the distribution of Ramanujan’s tau function
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by D. H. Lehmer PDF
Math. Comp. 24 (1970), 741-743 Request permission


According to a conjecture of Sato and Tate, the angle $\theta$ whose cosine is $\tfrac {1} {2}\tau (p){p^{ - 11/2}}$, where $\tau$ is Ramanujan’s function and $p$ a prime, is distributed over $[0,\pi ]$ according to a ${\sin ^2}\theta$ law. The paper reports on a test of this conjecture for the 1229 primes under 10000. Extreme values of $\theta$ are also given.
    Letter of J. P. Serre to author, June 1, 1964. D. H. Lehmer, Table of Ramanujan’s Function $\tau (n)$, 1963. Ms. of 164 pages of computer printout. UMT File.
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Additional Information
  • © Copyright 1970 American Mathematical Society
  • Journal: Math. Comp. 24 (1970), 741-743
  • MSC: Primary 10.41
  • DOI:
  • MathSciNet review: 0274401