Class Numbers of Orders in Quartic Fields

Details Class Numbers of Orders in Quartic Fields Class Numbers of Orders in Quartic Fields

2006-05-04

arxiv.org/abs/math/0605111v1

Mathematics

Number Theory

LATeX, 24 pages

Scientific paper

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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