Uniform Bounds on S-Integral Torsion Points for $\mathbb{G}_m$ and Elliptic Curves
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866918313108439040 |
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| author | Yap, Jit Wu |
| author_facet | Yap, Jit Wu |
| contents | Let $K$ be a number field, $S$ a finite set of places. For $\mathbb{G}_m$ or an elliptic curve $E$ defined over $K$, we establish uniformity results on the number of $S$-integral torsion points relative to a non-torsion point $β$, as $β$ varies over number fields of bounded degree. In particular for $\mathbb{G}_m$, if $D$ is a positive integer, we prove a uniform bound on the degree of a torsion point $ζ$ that is $S$-integral relative to a non-torsion point $β$ with degree $\leq D$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_01562 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Uniform Bounds on S-Integral Torsion Points for $\mathbb{G}_m$ and Elliptic Curves Yap, Jit Wu Number Theory Dynamical Systems Let $K$ be a number field, $S$ a finite set of places. For $\mathbb{G}_m$ or an elliptic curve $E$ defined over $K$, we establish uniformity results on the number of $S$-integral torsion points relative to a non-torsion point $β$, as $β$ varies over number fields of bounded degree. In particular for $\mathbb{G}_m$, if $D$ is a positive integer, we prove a uniform bound on the degree of a torsion point $ζ$ that is $S$-integral relative to a non-torsion point $β$ with degree $\leq D$. |
| title | Uniform Bounds on S-Integral Torsion Points for $\mathbb{G}_m$ and Elliptic Curves |
| topic | Number Theory Dynamical Systems |
| url | https://arxiv.org/abs/2302.01562 |