Distribution of zeta zeroes for abelian covers of algebraic curves over a finite field

2013/01/30 by Xiong, Maosheng
#11G20 #11M38 #11T55 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1301.7124

Abstract

For a function field k over a finite field with \mathbbF_q as the field of constant, and a finite abelian group G whose exponent is divisible by q-1, we study the distribution of zeta zeroes for a random G-extension of k, ordered by the degree of conductors. We prove that when the degree goes to infinity, the number of zeta zeroes lying in a prescribed arc is uniformly distributed and the variance follows a Gaussian distribution.

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