Hyperkloosterman sums revisited

2019/11/24 by Alan Adolphson, Steven Sperber, Adolphson, Alan +1
Mathematics · #Advanced Algebra and Geometry #Advanced Mathematical Identities #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1911.10639

openalex publication_date 2019/11/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We return to some past studies of hyperkloosterman sums ([9,10]) via p-adic cohomology with an aim to improve earlier results. In particular, we work here with Dwork's θ_∞-splitting function and a better choice of basis for cohomology. To a large extent, we are guided to this choice of basis by our recent work on the p-integrality of coefficients of A-hypergeometric series[3]. In the earlier work, congruence estimates were limited to p>n+2. We are here able to remove all characteristic restrictions from earlier results.

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