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
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.