The circle method and pointwise ergodic theorems
Dynamical Systems
2026-02-13 v1 Classical Analysis and ODEs
Number Theory
Abstract
The purpose of this article is to discuss the circle method and its quantitative role in understanding pointwise almost everywhere convergence phenomena for polynomial ergodic averaging operators. Specifically, we will use the circle method to illustrate that pointwise almost everywhere convergence and norm convergence in ergodic theory can have fundamentally different natures. More importantly, these differences may necessitate the use of distinct types of tools, which can sometimes be more intriguing than the original problems themselves.
Cite
@article{arxiv.2602.11344,
title = {The circle method and pointwise ergodic theorems},
author = {Mariusz Mirek},
journal= {arXiv preprint arXiv:2602.11344},
year = {2026}
}
Comments
20 pages, no figures, to appear in the Proceedings of the ICM 2026