Effective Kummer Theory for Elliptic Curves
نویسندگان
چکیده
Abstract Let $E$ be an elliptic curve defined over a number field $K$, let $\alpha \in E(K)$ point of infinite order, and $N^{-1}\alpha $ the set $N$-division points in $E(\overline {K})$. We prove strong effective uniform results for degrees Kummer extensions $[K(E[N],N^{-1}\alpha ): K(E[N])]$. When $K=\mathbb Q$, under minimal (necessary) assumption on $, we show that inequality $[\mathbb Q(E[N],N^{-1}\alpha \mathbb Q(E[N])] \geq cN^2$ holds positive constant $c$ independent both $.
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ژورنال
عنوان ژورنال: International Mathematics Research Notices
سال: 2021
ISSN: ['1687-0247', '1073-7928']
DOI: https://doi.org/10.1093/imrn/rnab216