An effective Deligne's equidistribution theorem

TL;DR

This paper establishes an effective version of Deligne's equidistribution theorem by proving an Erdős–Turán type inequality for compact Lie groups, enabling quantitative analysis of distribution properties.

Contribution

It introduces an effective approach to Deligne's theorem through a novel Erdős–Turán inequality tailored for compact Lie groups.

Findings

Derived an explicit inequality for compact Lie groups

Provided a quantitative version of Deligne's equidistribution theorem

Enhanced understanding of distribution properties in algebraic geometry

Abstract

We prove an Erd\H{o}s--Tur\'an type inequality for compact Lie groups, from which we deduce an effective version of Deligne's equidistribution theorem.