Bucur, Alina; David, Chantal; Feigon, Brooke; Lalín, Matilde; Sinha, Kaneenika Distribution of zeta zeroes of Artin-Schreier covers. (English) Zbl 1348.11048 Math. Res. Lett. 19, No. 6, 1329-1356 (2012). Summary: We study the distribution of the zeros 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 \([-\pi,\pi)\) has a standard Gaussian distribution (when properly normalized). Cited in 1 ReviewCited in 7 Documents MSC: 11G20 Curves over finite and local fields 11M50 Relations with random matrices 14G15 Finite ground fields in algebraic geometry Keywords:Artin-Schreier cover; projective line; zeta zeros; mesoscopic regime PDFBibTeX XMLCite \textit{A. Bucur} et al., Math. Res. Lett. 19, No. 6, 1329--1356 (2012; Zbl 1348.11048) Full Text: DOI arXiv Link