Equidistribution of nilflows and bounds on Weyl sums
Dynamical Systems
2025-10-03 v3 Number Theory
Abstract
We prove an effective equidistribution result for a class of higher step nilflows, called filiform nilflows, and derive bounds on Weyl sums for higher degree polynomials with a power saving comparable to the best known, derived by J. Bourgain, C. Demeter and L. Guth and by T. Wooley from their proof of Vinogradov Main Conjecture. Our argument is based on ideas from dynamical systems (cohomological equations, invariant distributions) and on non-Abelian harmonic analysis.
Keywords
Cite
@article{arxiv.2302.03618,
title = {Equidistribution of nilflows and bounds on Weyl sums},
author = {Livio Flaminio and Giovanni Forni},
journal= {arXiv preprint arXiv:2302.03618},
year = {2025}
}
Comments
Lemmas 3.11 and 3.12 (for strongly adapted bases) wrongly applied in Lemma 5.6 (for adapted bases)