English

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 pp-adic analytic properties of the height zeta function. In particular, we will show that for a large class of projective varieties this function is pp-adic meromorphic.

Keywords

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}
}
R2 v1 2026-06-21T08:22:21.818Z