Finite hypergeometric functions
Number Theory
2018-04-12 v2
Abstract
Finite hypergeometric functions are complex valued functions on finite fields which are the analogue of the classical analytic hypergeometric functions. From the work of N.M.Katz it follows that their values are traces of Frobenius on certain l-adic sheafs. More concretely, in many instances their values can be used to give formulas for pointcounts of F_q-rational points on certain varieties. In this paper we work out the case of one-variable functions whose monodromy in the analytic case can be defined over the rational integers.
Cite
@article{arxiv.1505.02900,
title = {Finite hypergeometric functions},
author = {Frits Beukers and Henri Cohen and Anton Mellit},
journal= {arXiv preprint arXiv:1505.02900},
year = {2018}
}
Comments
26 pages, 2 figures