A lower bound on the proportion of modular elliptic curves over Galois CM fields

2022/03/01 by Feng, Zachary
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2203.00731

Abstract

We calculate an explicit lower bound on the proportion of elliptic curves that are modular over any Galois CM field not containing ζ₅. Applied to imaginary quadratic fields, this proportion is at least 2/5. Applied to cyclotomic fields ℚ(ζ_n) with 5\nmid n, this proportion is at least 1-ε with only finitely many exceptions of n, for any choice of ε > 0.

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