Moment transference principles and multiplicative diophantine approximation on hypersurfaces
Number Theory
2025-04-18 v2
Abstract
We determine the generic multiplicative approximation rate on a hypersurface. There are four regimes, according to convergence or divergence and curved or flat, and we address all of them. Using geometry and arithmetic in Fourier space, we develop a general framework of moment transference principles, which convert Lebesgue data into data for some other measure.
Cite
@article{arxiv.2408.10911,
title = {Moment transference principles and multiplicative diophantine approximation on hypersurfaces},
author = {Sam Chow and Han Yu},
journal= {arXiv preprint arXiv:2408.10911},
year = {2025}
}