The Normal Distribution as a Limit of Generalized Sato-Tate Measures
Number Theory
2008-10-14 v1
Abstract
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.
Keywords
Cite
@article{arxiv.0810.2012,
title = {The Normal Distribution as a Limit of Generalized Sato-Tate Measures},
author = {Michael Larsen},
journal= {arXiv preprint arXiv:0810.2012},
year = {2008}
}
Comments
This is an unpublished preprint from the mid-1990s. Much of it has been superseded since. Plain TeX, 15 pages