Class Numbers of Orders in Quartic Fields
classification
🧮 math.NT
keywords
fieldsnumberclasscomplexnumbersquarticasymptoticcase
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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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