Distribution of zeta zeroes of Artin--Schreier curves

Details Distribution of zeta zeroes of Artin--Schreier curves Distribution of zeta zeroes of Artin--Schreier curves

2011-11-20

arxiv.org/abs/1111.4701v1

Mathematics

Number Theory

Scientific paper

We study the distribution of the zeroes of the zeta functions of the family of Artin-Schreier curves over $\mathbb{F}_q$ when $q$ is fixed and the genus goes to infinity. We consider both the global and the mesoscopic regimes, proving that when the genus goes to infinity, the number of zeroes with angles in a prescribed interval of $[-\pi,\pi)$ has a standard Gaussian distribution (when properly normalized).

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