Averages of arithmetic functions over polynomials in many variables
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
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| _version_ | 1866929516303089664 |
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| author | Destagnol, Kevin Sofos, Efthymios |
| author_facet | Destagnol, Kevin Sofos, Efthymios |
| contents | We estimate the average of any arithmetic function $k$ over the values of any smooth polynomial in many variables provided only that $k$ has a distribution in arithmetic progressions of fixed modulus.
We give several applications of this result including the analytic Hasse principle for an intersection of two cubics in 21 variables and asymptotics for the number of integer solutions of a non-algebraic variety. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_18116 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Averages of arithmetic functions over polynomials in many variables Destagnol, Kevin Sofos, Efthymios Number Theory We estimate the average of any arithmetic function $k$ over the values of any smooth polynomial in many variables provided only that $k$ has a distribution in arithmetic progressions of fixed modulus. We give several applications of this result including the analytic Hasse principle for an intersection of two cubics in 21 variables and asymptotics for the number of integer solutions of a non-algebraic variety. |
| title | Averages of arithmetic functions over polynomials in many variables |
| topic | Number Theory |
| url | https://arxiv.org/abs/2409.18116 |