Contents Online
Mathematical Research Letters
Volume 19 (2012)
Number 6
Distribution of zeta zeroes of Artin–Schreier covers
Pages: 1329 – 1356
DOI: https://dx.doi.org/10.4310/MRL.2012.v19.n6.a12
Authors
Abstract
We study the distribution of the zeroes of the zeta functions of the family of Artin–Schreier covers of the projective line 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 non-trivial subinterval of $[−π, π)$ has a standard Gaussian distribution (when properly normalized).
2010 Mathematics Subject Classification
Primary 11G20. Secondary 11M50, 14G15.
Published 18 July 2013