On an inequality of Bushnell--Henniart for Rankin--Selberg conductors

TL;DR

This paper establishes a division algebra analogue of a key ultrametric inequality related to Rankin--Selberg conductors, showing their equivalence under the Jacquet--Langlands correspondence.

Contribution

It introduces a new division algebra analogue of Bushnell--Henniart's inequality and demonstrates its equivalence to the original through Jacquet--Langlands correspondence.

Findings

Proves a division algebra analogue of Bushnell--Henniart's inequality.

Shows the equivalence of the two inequalities under Jacquet--Langlands correspondence.

Enhances understanding of conductors in the context of division algebras.

Abstract

We prove a division algebra analogue of an ultrametric inequality of Bushnell--Henniart for Rankin--Selberg conductors. Under the Jacquet--Langlands correspondence, the two versions are equivalent.