T-adic Exponential Sums over Affinoids

2019/01/16 by Matthew Schmidt, Schmidt, Matthew
Mathematics · #Advanced Mathematical Identities #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1901.05516

openalex publication_date 2019/01/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce and develop (π,p)-adic Dwork theory for L-functions of exponential sums associated to one-variable rational functions, interpolating p^k-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 C-function C_f(s,π). We compute the lower (π,p)-adic bound, the Hodge polygon, for this C-function. Along the way, we also show why a strictly π-adic theory will not work in this case.

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