An Erdos-Turan Inequality For Compact Simply-Connected Semisimple Lie Groups

TL;DR

This paper extends the Erdős-Turán inequality to compact simply-connected semisimple Lie groups, providing bounds on how far sequences are from equidistribution based on character moments.

Contribution

It introduces a novel inequality for Lie groups that generalizes the classical Erdős-Turán inequality from the circle to more complex group structures.

Findings

Established an inequality relating character moments to equidistribution in Lie groups

Generalized classical results from circle to semisimple Lie groups

Provides tools for analyzing distribution properties in advanced algebraic structures

Abstract

The classical Erd{\" o}s-Turan Inequality bounds how far a sequence of points in the circle is from being equidistributed in terms of its exponential moments. We prove an analogous inequality for all compact simply-connected semisimple Lie groups, bounding how far a sequence is from being equidistributed in the conjugacy classes of the group in terms of the moments of irreducible characters.