摘要
The Hilbert genus field of the real biquadratic field K=Q（√δ,√d）is described by Yue（2010）and Bae and Yue（2011）explicitly in the case＆=2 or p with p=1 mod 4 a prime and d a squarefree positive integer.In this article,we describe explicitly the Hilbert genus field of the imaginary biquadratic field K=Q（√δ,√d）,whereδ=-1,-2 or-p with p=3 mod 4 a prime and d any squarefree integer.This completes the explicit construction of the Hilbert genus field of any biquadratic field which contains an imaginary quadratic subfield of odd class number.
The Hilbert genus field of the real biquadratic field K=Q(δ^(1/2),d^(1/2)is described by Yue(2010)and Bae and Yue(2011)explicitly in the case&=2 or p with p=1 mod 4 a prime and d a squarefree positive integer.In this article,we describe explicitly the Hilbert genus field of the imaginary biquadratic field K=Q(δ^(1/2),d^(1/2)),whereδ=-1,-2 or-p with p=3 mod 4 a prime and d any squarefree integer.This completes the explicit construction of the Hilbert genus field of any biquadratic field which contains an imaginary quadratic subfield of odd class number.
基金
supported by National Key Basic Research Program of China(Grant No.2013CB834202)
National Natural Science Foundation of China(Grant No.11171317)
