Imaginary Multiquadratic Fields of Class Number Dividing 2^m

2017/12/19 by Feaver, Amy, Puskas, Anna
#11R04 #11R29 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1712.06769

Abstract

This paper gives a method to find all imaginary multiquadratic fields of class number dividing 2^m, provided the list of all imaginary quadratic fields of class number dividing 2^m+1 is known. We give a bound on the degree of such fields. As an application of this algorithm, we compute a complete list of imaginary multiquadratic fields with class number dividing 32.

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• Imaginary Multiquadratic Fields of Class Number 1
• Imaginary multiquadratic number fields of exponent 3 and 5
• Class numbers of Imaginary bicyclic biquadratic number fields
• The number of imaginary quadratic fields with a given class number
• Notes on the divisibility of the class numbers of certain imaginary quadratic fields