Lehmer-Type bounds and counting rational points of bounded heights on Abelian varieties
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866916480871825408 |
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| author | Kumar, Narasimha Sahoo, Satyabrat |
| author_facet | Kumar, Narasimha Sahoo, Satyabrat |
| contents | In this article, we study Lehmer-type bounds for the Néron-Tate height of $\bar{K}$-points on abelian varieties $A$ over number fields $K$. Then, we estimate the number of $K$-rational points on $A$ with Néron-Tate height $\leq \log B$ for $B\gg 0$. This estimate involves a constant $C$, which is not explicit. However, for elliptic curves and the product of elliptic curves over $K$, we make the constant explicitly computable. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2311_11266 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Lehmer-Type bounds and counting rational points of bounded heights on Abelian varieties Kumar, Narasimha Sahoo, Satyabrat Number Theory (MSC 2020) Primary 11G50, 11G10, 14K15, Secondary 14G25 In this article, we study Lehmer-type bounds for the Néron-Tate height of $\bar{K}$-points on abelian varieties $A$ over number fields $K$. Then, we estimate the number of $K$-rational points on $A$ with Néron-Tate height $\leq \log B$ for $B\gg 0$. This estimate involves a constant $C$, which is not explicit. However, for elliptic curves and the product of elliptic curves over $K$, we make the constant explicitly computable. |
| title | Lehmer-Type bounds and counting rational points of bounded heights on Abelian varieties |
| topic | Number Theory (MSC 2020) Primary 11G50, 11G10, 14K15, Secondary 14G25 |
| url | https://arxiv.org/abs/2311.11266 |