Convergence of orbital integrals on unitary groups in positive characteristic

TL;DR

This paper proves that orbital integrals on unitary groups over non-archimedean local fields converge absolutely in positive characteristic, advancing understanding in harmonic analysis.

Contribution

It establishes the absolute convergence of orbital integrals on unitary groups in positive characteristic, a result previously unconfirmed in this setting.

Findings

Orbital integrals are absolutely convergent in positive characteristic.

The proof applies to non-archimedean local fields.

This result supports harmonic analysis on unitary groups.

Abstract

We prove the absolute convergence of orbital integrals on a unitary group over a non-archimedean local field in any positive characteristic.