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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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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

Abstract:

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.
References
    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: https://doi.org/10.1090/S0025-5718-1970-0274401-8
  • MathSciNet review: 0274401