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arXiv · 2206.12860

Modularity of elliptic curves over cyclotomic $\mathbb{Z}_p$-extensions of real quadratic fields

Sho Yoshikawa
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Abstract

We prove that all elliptic curves defined over the cyclotomic $\mathbb{Z}_p$-extension of a real quadratic field are modular under the assumption that the algebraic part of the central value of a twisted $L$-function is a $p$-adic unit. Our result is a generalization of a result of X. Zhang, which is a real quadratic analogue of a result of Thorne.

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Sho Yoshikawa. 2022-06-26. Modularity of elliptic curves over cyclotomic $\mathbb{Z}_p$-extensions of real quadratic fields. https://arxiv.org/abs/2206.12860

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