EXPLICIT DETERMINATION OF GL(n) KLOOSTERMAN SUMS

Certain exponential sums arise when one computes the Fourier expansion of a GL(n) Poincaré series; these sums are thus GL(n) analogues of the classical Kloosterman sum (n = 2), and the sums found for GL(3) by Bump, the author and Goldfeld. They are defined in group theoretic terms. In this note a pr...

Full description

Saved in:
Bibliographic Details
Published inSéminaire de Théorie des Nombres de Bordeaux pp. 1 - 22
Main Author Friedberg, Solomon
Format Journal Article
LanguageEnglish
Published université de bordeaux I, u.e.r. de mathématiques et d'informatique 01.01.1985
Subjects
Continuous spectra
Coordinate systems
Fourier coefficients
Fourier series
Fourier series expansion
Inner products
Preprints
Series expansion
Online AccessGet full text

Cover

More Information
Summary:Certain exponential sums arise when one computes the Fourier expansion of a GL(n) Poincaré series; these sums are thus GL(n) analogues of the classical Kloosterman sum (n = 2), and the sums found for GL(3) by Bump, the author and Goldfeld. They are defined in group theoretic terms. In this note a procedure is explained for writing them in elementary terms (sums of exponentials and congruence conditions), using certain "Plücker coordinates". This is illustrated with an example from GL(4). The relation between these sums and automorphic forms on GL(4) is also considered, and in particular, it is shown that the partial Kloosterman zeta function corresponding to the element (I₃ ¹) of the Weyl group does not have region of absolute convergence corresponding to the Ramanujan-Petersson conjecture; this is in contradistinction to the GL(3) case.
ISSN:0989-5558
2547-5819