The Normal Distribution as a Limit of Generalized Sato-Tate Measures

Mathematics – Number Theory

Scientific paper

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This is an unpublished preprint from the mid-1990s. Much of it has been superseded since. Plain TeX, 15 pages

Scientific paper

With suitable order of limits, as p, m, and n all tend to infinity, the
distribution of the normalized trace of Frobenius on H^1 of a "random" plane
curve of degree n over the field with p^m elements, tends to a Gaussian
distribution. The same is true of a "random" curve of genus g over the field
with p^m elements.

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