On the Instability of the Riemann Hypothesis over Finite Fields
Complex Variables
2010-08-04 v1
Abstract
We show that it is possible to approximate the zeta-function of a curve over a finite field by meromorphic functions which satisfy the same functional equation and moreover satisfy (respectively do not satisfy) the analogue of the Riemann hypothesis. In the other direction, it is possible to approximate holomorphic functions by simple manipulations of such a zeta-function. We also consider the value distribution of zeta-functions of function fields over finite fields from the viewpoint of Nevanlinna theory.
Keywords
Cite
@article{arxiv.1008.0499,
title = {On the Instability of the Riemann Hypothesis over Finite Fields},
author = {P. M. Gauthier and N. Tarkhanov},
journal= {arXiv preprint arXiv:1008.0499},
year = {2010}
}
Comments
16 pages