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Main Authors: Kowalski, Emmanuel, Untrau, Théo
Format: Preprint
Published: 2025
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Online Access:https://arxiv.org/abs/2505.22059
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author Kowalski, Emmanuel
Untrau, Théo
author_facet Kowalski, Emmanuel
Untrau, Théo
contents The Wasserstein distance between probability measures on compact spaces provides a natural invariant quantitative measure of equidistribution, which is partly similar to the classical discrepancy appearing in Erdös-Turán type inequalities in the case of tori, but is a more intrinsic quantity. We recall the basic properties of Wasserstein distances and present applications to quantitative forms of equidistribution of exponential sums in two examples, one related to our previous work on the equidistribution of ultra-short exponential sums, and the second a quantitative form of the equidistribution theorems of Deligne and Katz.
format Preprint
id arxiv_https___arxiv_org_abs_2505_22059
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Wasserstein metrics and quantitative equidistribution of exponential sums over finite fields
Kowalski, Emmanuel
Untrau, Théo
Number Theory
11K38, 11L03, 11T23, 49Q22
The Wasserstein distance between probability measures on compact spaces provides a natural invariant quantitative measure of equidistribution, which is partly similar to the classical discrepancy appearing in Erdös-Turán type inequalities in the case of tori, but is a more intrinsic quantity. We recall the basic properties of Wasserstein distances and present applications to quantitative forms of equidistribution of exponential sums in two examples, one related to our previous work on the equidistribution of ultra-short exponential sums, and the second a quantitative form of the equidistribution theorems of Deligne and Katz.
title Wasserstein metrics and quantitative equidistribution of exponential sums over finite fields
topic Number Theory
11K38, 11L03, 11T23, 49Q22
url https://arxiv.org/abs/2505.22059