On Linnik and Selberg’s conjecture about sums of Kloosterman sums

Peter Sarnak, Jacob Tsimerman

Research output: Chapter in Book/Report/Conference proceedingChapter

9 Scopus citations

Abstract

We examine the Linnik and Selberg Conjectures concerning sums of Kloosterman sums, in all its aspects (x, m and n). We correct the precise form of the Conjecture and establish an analogue of Kuznetzov’s 1/6 exponent in the mn aspect. This, perhaps somewhat surprisingly, is connected with the transional ranges associated with asymptotics of Bessel Functions of large order.

Original languageEnglish (US)
Title of host publicationProgress in Mathematics
PublisherSpringer Basel
Pages619-635
Number of pages17
DOIs
StatePublished - Jan 1 2009

Publication series

NameProgress in Mathematics
Volume270
ISSN (Print)0743-1643
ISSN (Electronic)2296-505X

All Science Journal Classification (ASJC) codes

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology

Keywords

  • Kloosterman sums
  • Kuznetzov formula
  • Ramanujan-Selberg conjectures

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    Sarnak, P., & Tsimerman, J. (2009). On Linnik and Selberg’s conjecture about sums of Kloosterman sums. In Progress in Mathematics (pp. 619-635). (Progress in Mathematics; Vol. 270). Springer Basel. https://doi.org/10.1007/978-0-8176-4747-6_20