Affiliation:
1. Department of Mathematics & Statistics , University of Maine System , Orono , ME 04469 , USA
Abstract
Abstract
A formula of Kuznetsov allows one to interpret a smooth sum of Kloosterman sums as a sum over the spectrum of
GL
(
2
)
{\operatorname{GL}(2)}
automorphic forms.
In this paper, we construct a similar formula for the first hyper-Kloosterman sums using
GL
(
3
)
{\operatorname{GL}(3)}
automorphic forms, resolving a long-standing problem of Bump, Friedberg and Goldfeld.
Along the way, we develop what are apparently new bounds for the order derivatives of the classical J-Bessel function, and we conclude with a discussion of the original method of Bump, Friedberg and Goldfeld.
Subject
Applied Mathematics,General Mathematics