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arXiv · 2005.07909

Analytic ranks of elliptic curves over number fields

Peter J. Cho
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Abstract

Let $E$ be an elliptic curve over $\mathbb{Q}$. Then, we show that the average analytic rank of $E$ over cyclic extensions of degree $l$ over $\mathbb{Q}$ with $l$ a prime not equal to $2$, is at most $2+r_{\mathbb{Q}}(E)$, where $r_{\mathbb{Q}}(E)$ is the analytic rank of the elliptic curve $E$ over $\mathbb{Q}$. This bound is independent of the degree $l$ Also, we also obtain some average analytic rank results over $S_d$-fields.

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Peter J. Cho. 2020-05-16. Analytic ranks of elliptic curves over number fields. https://arxiv.org/abs/2005.07909

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