### Class numbers of imaginary quadratic fields

Heilbronn Number Theory Seminar

14th March 2018, 4:00 pm – 5:00 pm

Howard House, 4th Floor Seminar Room

I will describe a result from my thesis in which I quantify a theorem of Wiles. I prove 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 almost any given finite 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. The proof relies on the theory of harmonic Maass forms, which are a type of real-analytic modular form. I will also discuss an application to twists of certain elliptic curves.

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