In this paper it is shown that a refinement on the weighted Hilbert inequalityfor double series can be established by introducing a proper non-zero real number R_ω.The expression of R_ω is given by means of the posi...In this paper it is shown that a refinement on the weighted Hilbert inequalityfor double series can be established by introducing a proper non-zero real number R_ω.The expression of R_ω is given by means of the positive definiteness of a Gram matrix.展开更多
For quadratic number ?elds F = Q(√2p1 ···pt?1 ) with primes pj ≡ 1 mod 8, the authors study the class number and the norm of the fundamental unit of F. The resultsgeneralize nicely what has been famil...For quadratic number ?elds F = Q(√2p1 ···pt?1 ) with primes pj ≡ 1 mod 8, the authors study the class number and the norm of the fundamental unit of F. The resultsgeneralize nicely what has been familiar for the ?elds Q(√2p) with a prime p ≡ 1 mod 8, including density statements. And the results are stated in terms of the quadratic form x2 + 32y2 and illustrated in terms of graphs.展开更多
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...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.展开更多
文摘In this paper it is shown that a refinement on the weighted Hilbert inequalityfor double series can be established by introducing a proper non-zero real number R_ω.The expression of R_ω is given by means of the positive definiteness of a Gram matrix.
基金Project supported by the National Natural Science Foundation of China (No.10371054) and 02KJB11006.
文摘For quadratic number ?elds F = Q(√2p1 ···pt?1 ) with primes pj ≡ 1 mod 8, the authors study the class number and the norm of the fundamental unit of F. The resultsgeneralize nicely what has been familiar for the ?elds Q(√2p) with a prime p ≡ 1 mod 8, including density statements. And the results are stated in terms of the quadratic form x2 + 32y2 and illustrated in terms of graphs.
基金supported by National Key Basic Research Program of China(Grant No.2013CB834202)National Natural Science Foundation of China(Grant No.11171317)
文摘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.
