Vol. 300, No. 2, 2019

Download this article
Download this article For screen
For printing
Recent Issues
Vol. 300: 1  2
Vol. 299: 1  2
Vol. 298: 1  2
Vol. 297: 1  2
Vol. 296: 1  2
Vol. 295: 1  2
Vol. 294: 1  2
Vol. 293: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Subscriptions
Editorial Board
Officers
Special Issues
Submission Guidelines
Submission Form
Contacts
Author Index
To Appear
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Other MSP Journals
On the Braverman–Kazhdan proposal for local factors: spherical case

Zhilin Luo

Vol. 300 (2019), No. 2, 431–471
Abstract

We study the Braverman–Kazhdan proposal for the local spherical situation. In the p-adic case, we give a definition of the spherical component of conjectural space Sρ(G,K) and the ρ-Fourier transform kernel ΦρK, and verify several conjectures of Braverman and Kazhdan (GAFA 2000 special volume, part I, 237–278) in this situation. In the archimedean case, we study the asymptotic of the basic function 1ρ,s and the ρ-Fourier transform kernel Φρ,sK.

Keywords
L-function, Fourier transform, Schwartz space
Mathematical Subject Classification 2010
Primary: 11F70, 22E45
Secondary: 22E35
Milestones
Received: 14 March 2018
Revised: 13 September 2018
Accepted: 13 September 2018
Published: 30 July 2019
Authors
Zhilin Luo
School of Mathematics
University of Minnesota
Minneapolis, MN 55455
United States