Kloosterman Sums and their Applications: A Review
Copyright policy )Kloosterman Sums and their Applications: A Review
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.
Kuznetsov sum formula, Spectral theory; trace formulas (e.g., that of Selberg), cofinite discrete groups, Sato-Tate conjecture, automorphic forms, Selberg trace formula, exceptional eigenvalues, Kloosterman sums, holomorphic modular forms, Hecke operators, Selberg conjecture, Selberg-Kloosterman zeta function, Gauss and Kloosterman sums; generalizations, Holomorphic modular forms of integral weight, Ramanujan-Petersson conjecture, Forms of half-integer weight; nonholomorphic modular forms, representation of the adeles
Kuznetsov sum formula, Spectral theory; trace formulas (e.g., that of Selberg), cofinite discrete groups, Sato-Tate conjecture, automorphic forms, Selberg trace formula, exceptional eigenvalues, Kloosterman sums, holomorphic modular forms, Hecke operators, Selberg conjecture, Selberg-Kloosterman zeta function, Gauss and Kloosterman sums; generalizations, Holomorphic modular forms of integral weight, Ramanujan-Petersson conjecture, Forms of half-integer weight; nonholomorphic modular forms, representation of the adeles
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