4-ranks of class groups of biquadratic fields

Abstract: Let K be a quadratic number field, and consider the family of biquadratic fields $K_n= K(\sqrt{n})$ for $n$ a squarefree integer. I will discuss joint work with Peter Koymans and Harry Smit in which we study, as $n$ varies, the 4-rank of the class group of $K_n$, showing in particular that for 100 % of squarefree n, the 4-rank is given by an explicit formula involving the number of prime divisors of n that are inert in $K$. If time permits I will discuss an elliptic curve analogue of this work, which is joint with Ross Paterson.

number theory

Audience: researchers in the topic

Heilbronn number theory seminar

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