$T$-adic Exponential Sums over Affinoids
Number Theory
2019-01-18 v1
Abstract
We introduce and develop -adic Dwork theory for -functions of exponential sums associated to one-variable rational functions, interpolating -order exponential sums over affinoids. Namely, we prove a generalization of the Dwork-Monsky-Reich trace formula and apply it to establish an analytic continuation of the -function . We compute the lower -adic bound, the Hodge polygon, for this -function. Along the way, we also show why a strictly -adic theory will not work in this case.
Cite
@article{arxiv.1901.05516,
title = {$T$-adic Exponential Sums over Affinoids},
author = {Matthew Schmidt},
journal= {arXiv preprint arXiv:1901.05516},
year = {2019}
}