A Kuznetsov formula for Kloosterman sums on \(\text{GL}_n\). (English) Zbl 1004.11047
The author considers finite weighted sums of Kloosterman sums on \(\text{GL}_n\) over the “denominators” and proves a generalization of the famous sum formula of N. V. Kuznetsov [Mat. Sb. 111(153), 334-383 (1980; Zbl 0427.10016)]. One motivation for a formula like this would be to show cancellations in sums of Kloosterman sums in the same way as Kuznetsov did in the classical case, but this would require a nontrivial estimate for the spectral side of the formula.
Reviewer: Matti Jutila (Turku)
MSC:
11L05 | Gauss and Kloosterman sums; generalizations |
11F70 | Representation-theoretic methods; automorphic representations over local and global fields |
22E55 | Representations of Lie and linear algebraic groups over global fields and adèle rings |