Modularity of elliptic curves over cyclotomic ℤ_p-extensions of real quadratic fields

2022/06/26 by Yoshikawa, Sho
#11G05(Primary) #11R23(Secondary) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2206.12860

Abstract

We prove that all elliptic curves defined over the cyclotomic 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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