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

Let $F$ be a global function field with constant field $𝔽_{q}$ . Let $G$ be a reductive group over $𝔽_{q}$ . 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 $ℙ_{𝔽_{q}}^{1}$ with two points of ramifications.

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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

Vol. 321, No. 1, 2022

Hongjie Yu

Abstract

PDF Access Denied

Keywords

Mathematical Subject Classification

Milestones

Authors