Let F = Q（x/P）, where p = 8t ＋ 1 is a prime. In this paper, we prove that a speclm case of Qin＇s conjecture on the possible structure of the 2-primary part of K2OF up to 8-rank is a consequence of a conjecture of ...Let F = Q（x/P）, where p = 8t ＋ 1 is a prime. In this paper, we prove that a speclm case of Qin＇s conjecture on the possible structure of the 2-primary part of K2OF up to 8-rank is a consequence of a conjecture of Cohen and Lagarias on the existence of governing fields. We also characterize the 16-rank of K2OF, which is either 0 or 1, in terms of a certain equation between 2-adic Hilbert symbols being satisfied or not.展开更多
In this paper, we discuss a method to compute the tame kernel of a number field. Confining ourselves to an imaginary quadratic field, we prove that _υ:K_2~S F/K_2~S F→k~* is bijective when N_υ>8δ_D^6.
基金Supported by NSFC(Grant Nos.11201225,11271177 and 11171141)
文摘Let F = Q（x/P）, where p = 8t ＋ 1 is a prime. In this paper, we prove that a speclm case of Qin＇s conjecture on the possible structure of the 2-primary part of K2OF up to 8-rank is a consequence of a conjecture of Cohen and Lagarias on the existence of governing fields. We also characterize the 16-rank of K2OF, which is either 0 or 1, in terms of a certain equation between 2-adic Hilbert symbols being satisfied or not.
文摘In this paper, we discuss a method to compute the tame kernel of a number field. Confining ourselves to an imaginary quadratic field, we prove that _υ:K_2~S F/K_2~S F→k~* is bijective when N_υ>8δ_D^6.
