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

 

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?)

  • [1] Letter of J. P. Serre to author, June 1, 1964.
  • [2] 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

DOI: http://dx.doi.org/10.1090/S0025-5718-1970-0274401-8
PII: S 0025-5718(1970)0274401-8
Keywords: Ramanujan's tau function, distribution
Article copyright: © Copyright 1970 American Mathematical Society