Class Numbers of Orders in Quartic Fields

Anton Deitmar; Mark Pavey

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Class Numbers of Orders in Quartic Fields

Anton Deitmar·Mark Pavey

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Abstract

We prove an asymptotic formula for class numbers of totlally imaginary quartic number fields, ie for number fields of degree 4 over Q with only complex embeddings. After previous work for real quadratic fields (Sarnak) and complex cubic fields (Deitmar), this is the last remaining case of number fields with unit rank one.

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Anton Deitmar, Mark Pavey. 2006-05-04. Class Numbers of Orders in Quartic Fields. https://arxiv.org/abs/math/0605111

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