A Nonstandard Approach to Equidistribution

TL;DR

This paper employs nonstandard analysis to extend classical equidistribution results to integrable functions and applies these findings to algebraic curves, linking to the Weil conjectures in characteristic zero.

Contribution

It introduces a nonstandard analytical method to generalize equidistribution theorems and connects these to algebraic geometry via the Weil conjectures.

Findings

Generalized equidistribution to integrable functions

Connected equidistribution with Weil conjectures

Extended classical results to new mathematical contexts

Abstract

Using nonstandard analysis, we generalise a classical result on equidistributions to integrable functions, and give an application of the Weil conjectures for algebraic curves, to equidistribution in characteristic zero.