Asymptotic properties of zeta functions over finite fields
Number Theory
2013-10-29 v2
Abstract
In this paper we study asymptotic properties of families of zeta and -functions over finite fields. We do it in the context of three main problems: the basic inequality, the Brauer--Siegel type results and the results on distribution of zeroes. We generalize to this abstract setting the results of Tsfasman, Vl\u{a}du\c{t} and Lachaud, who studied similar problems for curves and (in some cases) for varieties over finite fields. In the classical case of zeta functions of curves we extend a result of Ihara on the limit behaviour of the Euler--Kronecker constant. Our results also apply to -functions of elliptic surfaces over finite fields, where we approach the Brauer--Siegel type conjectures recently made by Kunyavskii, Tsfasman and Hindry.
Keywords
Cite
@article{arxiv.1310.6107,
title = {Asymptotic properties of zeta functions over finite fields},
author = {Alexey Zykin},
journal= {arXiv preprint arXiv:1310.6107},
year = {2013}
}