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A coarse geometric expansion of a variant of Arthur's truncated traces and some applications

Hongjie Yu

Vol. 321 (2022), No. 1, 193–237
Abstract

Let F be a global function field with constant field 𝔽q. Let G be a reductive group over 𝔽q. We establish a variant of Arthur’s truncated kernel for G and for its Lie algebra which generalises Arthur’s original construction. We establish a coarse geometric expansion for our variant truncation.

As applications, we consider some existence and uniqueness problems of some cuspidal automorphic representations for the functions field of the projective line 𝔽q1 with two points of ramifications.

Keywords
Arthur–Selberg trace formula, cuspidal automorphic representations, global function fields
Mathematical Subject Classification
Primary: 11F70, 11R58
Milestones
Received: 14 March 2022
Revised: 24 June 2022
Accepted: 29 August 2022
Published: 3 March 2023
Authors
Hongjie Yu
Institute of Science and Technology Austria
Klosterneuburg
Austria
Weizmann Institute of Science
Rehovot
Israel