A Cauchy-Schwarz inequality for representations of SU(2)

TL;DR

This paper introduces a Cauchy-Schwarz inequality tailored for representations of SU(2), motivated by applications in analyzing poles of L-functions, providing a new mathematical tool for representation theory and number theory.

Contribution

It presents a novel Cauchy-Schwarz inequality specifically for SU(2) representations, expanding the theoretical framework for analyzing L-functions.

Findings

Derived a new inequality for SU(2) representations

Applied the inequality to pole order calculations of L-functions

Enhanced understanding of representation-theoretic methods in number theory

Abstract

Motivated by some applications to calculating order of poles of certain (local or global) $L$-functions, the author considers a Cauchy-Schwarz type inequality for representations of SU(2).