Kloosterman sums and their applications: A review
type: Item
instance of: scholarly article
title: Kloosterman sums and their applications: A review
zbMATH Open document ID: 0852.11043
DOI: 10.1007/BF03322202
author: Norman E. Hurt
published in: Results in Mathematics
publication date: 1996-12-05T00:00:00Z
review text: This paper lists results, and explains some concepts and results, in the areas of automorphic forms (holomorphic as well as real analytic ones) for cofinite discrete groups of motions in the upper half plane, Kloosterman sums, Hecke operators, Selberg trace formula, Kuznetsov sum formula, representation of \(SL_2\) over the adeles. Its main usefulness seems to me that it gives this list, and pointers to the literature. In the introduction, the author states that Kloosterman sums are fundamental in quantum chaology. I have not found an explanation of this connection in the paper.
Mathematics Subject Classification ID: 11L05
Mathematics Subject Classification ID: 11F72
Mathematics Subject Classification ID: 11F11
Mathematics Subject Classification ID: 11F37
zbMATH DE Number: 872696
zbMATH Keywords: exceptional eigenvalues
zbMATH Keywords: holomorphic modular forms
zbMATH Keywords: Ramanujan-Petersson conjecture
zbMATH Keywords: Sato-Tate conjecture
zbMATH Keywords: Selberg conjecture
zbMATH Keywords: Selberg-Kloosterman zeta function
zbMATH Keywords: representation of the adeles
zbMATH Keywords: automorphic forms
zbMATH Keywords: cofinite discrete groups
zbMATH Keywords: Kloosterman sums
zbMATH Keywords: Hecke operators
zbMATH Keywords: Selberg trace formula
zbMATH Keywords: Kuznetsov sum formula
reviewed by: Roelof Bruggeman
MaRDI profile type: Publication
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