Local solubility in generalised Ch\^atelet varieties
Number Theory
2025-04-18 v2
Abstract
We develop a version of the Hardy-Littlewood circle method to obtain asymptotic formulas for averages of general multivariate arithmetic functions evaluated at polynomial arguments in several variables. As an application, we count the number of fibers with a rational point in families of high-dimensional Ch\^atelet varieties, allowing for arbitrarily large subordinate Brauer groups.
Cite
@article{arxiv.2504.11388,
title = {Local solubility in generalised Ch\^atelet varieties},
author = {Kevin Destagnol and Julian Lyczak and Efthymios Sofos},
journal= {arXiv preprint arXiv:2504.11388},
year = {2025}
}