Imaginary Bicyclic Biquadratic Number Fields with Class Number 5
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An imaginary bicyclic biquadratic number field K is a field of the form Q(√−m, √−n) where m and n are squarefree positive integers. The ideal class number hK of K is the order of the abelian group IK/PK, where IK and PK are the groups of fractional and principal fractional ideals in the ring of integers OK of K, respectively. This provides a measure on how far is OK from being a PID. We determine all imaginary bicyclic biquadratic number fields with class number 5. We show there are exactly 243 such fields.
Abstract
An imaginary bicyclic biquadratic number field K is a field of the form Q(√−m, √−n) where m and n are squarefree positive integers. The ideal class number hK of K is the order of the abelian group IK/PK, where IK and PK are the groups of fractional and principal fractional ideals in the ring of integers OK of K, respectively. This provides a measure on how far is OK from being a PID. We determine all imaginary bicyclic biquadratic number fields with class number 5. We show there are exactly 243 such fields.
참고문헌 (10)
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