Families of generalized Kloosterman sums

2013/07/07 by C. Douglas Haessig, Steven Sperber, Haessig, C. Douglas +1
Mathematics · #11L05 #14F30 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11L05 #msc:14F30

paper · pdf · doi:10.48550/arxiv.1307.1854

36 pages, 4 figures

arxiv created 2013/07/07 · openalex publication_date 2013/07/07 · arxiv updated 2013/07/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct p-adic relative cohomology for a family of toric exponential sums which generalize the classical Kloosterman sums. Under natural hypotheses such as quasi-homogeneity and nondegeneracy, this cohomology is acyclic except in the top dimension. Our construction enables sufficiently sharp estimates for the action of Frobenius on cohomology so that our earlier work may be applied to the L-functions coming from linear algebra operations on these families to deduce a number of basic properties.

Citations

• L-functions associated with families of toric exponential sums

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