Local solubility in generalised Châtelet varieties

2025/04/15 by Destagnol, Kevin, Lyczak, Julian, Sofos, Efthymios · 1 citation
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2504.11388

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 Châtelet varieties, allowing for arbitrarily large subordinate Brauer groups.

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