Stratification and averaging for exponential sums: bilinear forms with generalized Kloosterman sums
- Journal Article
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 Polya-Vinogradov range. This property is proved by a subtle interplay between etale cohomology in its algebraic and diophantine incarnations. We give a first application of our bilinear estimates concerning the first moment of a family of L-functions of degree 3. Show more
Journal / seriesAnnali della Scuola Normale Superiore di Pisa, Classe di Scienze
Pages / Article No.
PublisherScuola Normale Superiore
153647 - Geometric and Analytic Number Theory (SNF)
175755 - Geometric and Analytic Number Theory (SNF)
NotesThis article is published in the Special Issue volume 21.
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