Equidistribution of polynomial sequences in function fields, with applications

2013/11/04 by Thái Hoàng Lê, Yu-Ru Liu, Lê, Thái Hoàng +3 · 5 citations
Computer Science · Mathematics · #Analytic Number Theory Research #Coding theory and cryptography #FOS: Mathematics #Limits and Structures in Graph Theory #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1311.0892

openalex publication_date 2013/11/04 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We prove a function field analog of Weyl's classical theorem on equidistribution of polynomial sequences. Our result covers the case in which the degree of the polynomial is greater than or equal to the characteristic of the field, which is a natural barrier when applying the Weyl differencing process to function fields. We also discuss applications to van der Corput, intersective and Glasner sets in function fields.

Cited by

• Equidistribution of polynomial sequences in function fields: resolution of a conjecture
• A Weyl equidistribution theorem over function fields
• Polynomial actions of rings of integers of global fields and quasirandomness of Paley-type graphs
• Subconvex L^p-sets, Weyl's inequality, and equidistribution
• The asymptotic formula for Waring's problem in function fields

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