On the Braverman–Kazhdan proposal for local factors : spherical case

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 $S_{ρ} (G, K)$ and the $ρ$ -Fourier transform kernel $Φ_{ρ}^{K}$ , 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 $1_{ρ, s}$ and the $ρ$ -Fourier transform kernel $Φ_{ρ, s}^{K}$ .

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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

Vol. 300, No. 2, 2019

Zhilin Luo

Abstract

PDF Access Denied

Keywords

Mathematical Subject Classification 2010

Milestones

Authors