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 language | English (US) |
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Pages (from-to) | 1453-1530 |
Number of pages | 78 |
Journal | Annali della Scuola Normale Superiore di Pisa - Classe di Scienze |
Volume | 21 |
DOIs | |
State | Published - 2020 |
Externally published | Yes |
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Mathematics (miscellaneous)