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arXiv · 1612.04443

Indivisibility of class numbers of imaginary quadratic fields

Olivia Beckwith
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Abstract

We quantify a recent theorem of Wiles on class numbers of imaginary quadratic fields by proving an estimate for the number of negative fundamental discriminants down to -X whose class numbers are indivisible by a given prime and whose imaginary quadratic fields satisfy any given set of local conditions. This estimate matches the best results in the direction of the Cohen-Lenstra heuristics for the number of imaginary quadratic fields with class number indivisible by a given prime. This general result is applied to study rank 0 twists of certain elliptic curves.

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Olivia Beckwith. 2016-12-14. Indivisibility of class numbers of imaginary quadratic fields. https://arxiv.org/abs/1612.04443

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