On the $p$-adic meromorphy of the function field height zeta function
Number Theory
2007-05-23 v1 Algebraic Geometry
Abstract
In this brief note, we will investigate the number of points of bounded (twisted) height in a projective variety defined over a function field, where the function field comes from a projective variety of dimension greater than or equal to 2. A first step in this investigation is to understand the -adic analytic properties of the height zeta function. In particular, we will show that for a large class of projective varieties this function is -adic meromorphic.
Cite
@article{arxiv.0704.3410,
title = {On the $p$-adic meromorphy of the function field height zeta function},
author = {C. Douglas Haessig},
journal= {arXiv preprint arXiv:0704.3410},
year = {2007}
}