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

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