Stratification and averaging for exponential sums: bilinear forms with generalized Kloosterman sums

Emmanuel Kowalski, Philippe Michel, Will Sawin

Research output: Contribution to journalArticlepeer-review

15 Scopus citations

Abstract

We introduce a new comparison principle for exponential sums over finite fields in order to study "sum-product" sheaves that arise in the study of general bilinear forms with coefficients given by trace functions modulo a prime q. When these functions are hyper-Kloosterman sums with characters, we succeed in establishing cases of this principle that lead to non-trivial bounds below the Pólya-Vinogradov range. This property is proved by a subtle interplay between étale cohomology in its algebraic and diophantine incarnations.

Original languageEnglish (US)
Pages (from-to)1453-1530
Number of pages78
JournalAnnali della Scuola Normale Superiore di Pisa - Classe di Scienze
Volume21
DOIs
StatePublished - 2020
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Mathematics (miscellaneous)

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