Local solubility in generalised Châtelet varieties
Fuente:
arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
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| _version_ | 1866910913383104512 |
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| author | Destagnol, Kevin Lyczak, Julian Sofos, Efthymios |
| author_facet | Destagnol, Kevin Lyczak, Julian Sofos, Efthymios |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_11388 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Local solubility in generalised Châtelet varieties Destagnol, Kevin Lyczak, Julian Sofos, Efthymios Number Theory 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. |
| title | Local solubility in generalised Châtelet varieties |
| topic | Number Theory |
| url | https://arxiv.org/abs/2504.11388 |