Tamagawa numbers of quasi-split groups over function fields

TL;DR

This paper extends the computation of Tamagawa numbers to quasi-split groups over function fields using Morris' Eisenstein series theory, broadening the understanding of arithmetic invariants in algebraic groups.

Contribution

It introduces a method to compute Tamagawa numbers for quasi-split groups over function fields, expanding upon Harder's previous work for split groups.

Findings

Extended Tamagawa number calculations to quasi-split groups

Applied Morris' Eisenstein series theory in a new context

Provided explicit formulas for Tamagawa numbers in this setting

Abstract

We use Morris' theory of Eisenstein series for reductive groups over global function fields in order to extend Harder's computation of Tamagawa numbers to quasi-split groups.