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Imaginary Multiquadratic Fields of Class Number $2^k$ Feaver, Amy


(Joint work with Anna Puskas) We determine all of the imaginary $n$-quadratic fields with class number dividing 32 by extending on already known results for the class numbers of quadratic and biquadratic fields. Our results provide techniques to find complete lists of imaginary $n$-quadratic fields of class number $2^m$ for nonnegative integers $m$. Further, given a fixed $m>0$ we find a bound $B(m)$ on $n$ for which there are no imaginary $n$-quadratic fields of class number $2^m$ whenever $n>B(m)$.

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