On the Distribution of Points of Valuation 1 for a Polynomial in Two Variables
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866915811442032640 |
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| author | Rajkumar, Krishnan Shubham |
| author_facet | Rajkumar, Krishnan Shubham |
| contents | We investigate the variation in the total number of points in a random $p\times p$ square in $\mathbb{Z}^2$ where the $p$-adic valuation of a given polynomial in two variables is precisely $1$. We establish that this quantity follows a Poisson distribution as $p\rightarrow\infty$ under a certain conjecture. We also relate this conjecture to certain uniform distribution properties of a vector valued sequence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_05366 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Distribution of Points of Valuation 1 for a Polynomial in Two Variables Rajkumar, Krishnan Shubham Number Theory We investigate the variation in the total number of points in a random $p\times p$ square in $\mathbb{Z}^2$ where the $p$-adic valuation of a given polynomial in two variables is precisely $1$. We establish that this quantity follows a Poisson distribution as $p\rightarrow\infty$ under a certain conjecture. We also relate this conjecture to certain uniform distribution properties of a vector valued sequence. |
| title | On the Distribution of Points of Valuation 1 for a Polynomial in Two Variables |
| topic | Number Theory |
| url | https://arxiv.org/abs/2411.05366 |