Hyperkloosterman sums revisited

Alan Adolphson, Steven Sperber

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)328-351
Number of pages24
JournalJournal of Number Theory
StatePublished - Feb 2023

Bibliographical note

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© 2022 Elsevier Inc.


  • Deformation equation
  • Hyperkloosterman sum
  • p-adic Banach space


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