Class Numbers of Orders in Quartic Fields

2006/05/04 by Deitmar, Anton, Pavey, Mark
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.math/0605111

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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• Class Numbers of Orders in Quartic Fields
• Class numbers of orders in cubic fields
• A class number problem for imaginary cyclic number fields of 2-power degrees
• Class Number Formulas for Certain Biquadratic Fields
• The number of imaginary quadratic fields with a given class number