On a family of sparse exponential sums

Moubariz Z. Garaev, Zeev Rudnick, Igor E. Shparlinski

Research output: Contribution to journalArticlepeer-review

Abstract

We investigate exponential sums modulo primes whose phase function is a sparse polynomial, with exponents growing with the prime. In particular, such sums model those which appear in the study of the quantum cat map. While they are not amenable to treatment by algebro-geometric methods such as Weil's bounds, Bourgain gave a nontrivial estimate for these and more general sums. In this work, we obtain explicit bounds with reasonable savings over various types of averaging. We also initiate the study of the value distribution of these sums.

Original languageEnglish
Pages (from-to)4214-4231
Number of pages18
JournalMathematische Nachrichten
Volume297
Issue number11
DOIs
StatePublished - Nov 2024

Keywords

  • binomial exponential sums
  • moments
  • trinomial exponential sums

All Science Journal Classification (ASJC) codes

  • General Mathematics

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