Towards a nonstandard Fourier analysis in automorphic forms: Some results on two toy examples /

Saved in:
Bibliographic Details
Author / Creator:Cheng, Shuyang, author.
Ann Arbor : ProQuest Dissertations & Theses, 2016
Description:1 electronic resource (185 pages)
Format: E-Resource Dissertations
Local Note:School code: 0330
URL for this record:
Hidden Bibliographic Details
Other authors / contributors:University of Chicago. degree granting institution.
Notes:Advisors: Bao Chau Ngo; Paul E. Herman Committee members: Matthew J. Emerton; Bao Chau Ngo.
Dissertation Abstracts International, Volume: 77-10(E), Section: B.
Summary:This thesis consists of two main parts.
In the first part an integral transform between spaces of nonstandard test functions on the affine space of dimension n is constructed. The integral transform satisfies a summation formula of Poisson type, which is derived from an analogue of the Arthur-Selberg trace formula for the Lie algebra of n-by-n matrices.
In the second part a proof of Conjecture 9.12 of Braverman-Kazhdan in their article "gamma-functions of representations and lifting" on the acyclicity of their l-adic gamma-sheaves over certain affine spaces is given for GL(n).