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Note on the distribution of Ramanujan’s tau function

Author: D. H. Lehmer
Journal: Math. Comp. 24 (1970), 741-743
MSC: Primary 10.41
MathSciNet review: 0274401
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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 [Enhancements On Off] (What's this?)

    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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Keywords: Ramanujan’s tau function, distribution
Article copyright: © Copyright 1970 American Mathematical Society