English

A Weyl equidistribution theorem over function fields

Number Theory 2026-01-29 v2

Abstract

A classical theorem of Weyl states that any polynomial with an irrational coefficient other than the constant term is uniformly distributed mod 1. We prove a new function field analogue of this statement, confirming a conjecture of L\^{e}, Liu, and Wooley.

Keywords

Cite

@article{arxiv.2509.18789,
  title  = {A Weyl equidistribution theorem over function fields},
  author = {Ethan Ackelsberg},
  journal= {arXiv preprint arXiv:2509.18789},
  year   = {2026}
}

Comments

8 pages, to appear in Archiv der Mathematik. The statements of Theorems 2.1 and 3.2 have been corrected from the previous version, as explained in Remark 2.2