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Local solubility in generalised Ch\^atelet varieties

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arxiv 2504.11388 v2 pith:HVRLR2AG submitted 2025-04-15 math.NT

Kevin Destagnol , Julian Lyczak , Efthymios Sofos This is my paper · ORCID
classification math.NT
keywords ateletvarietiesallowingapplicationarbitrarilyargumentsarithmeticasymptotic
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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.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. An improved large sieve for quadratic characters via Hooley neutralisers and its applications

    math.NT 2025-06 conditional novelty 7.0 of 10

    Using Hooley neutralisers, a large sieve for quadratic characters is improved for multiplicatively weighted sequences, with applications to hyperbolic-region character sums.

  2. Solubility of a family of conics with polynomial coefficients in many variables

    math.NT 2025-11 reject novelty 6.0 of 10

    An asymptotic for the density of soluble conics with polynomial coefficients is proposed, but the sign decomposition (6.5) that bridges the circle-method counts to the true count is false.

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