Unramified quadratic extensions of real quadratic fields, normal integral bases, and 2-adic L-functions

[摘要] Let K=Q(root m) be a real quadratic number field. In this article, we find a necessary and sufficient condition for K to admit an unramified quadratic extension with a normal integral basis distinct from K(root-1), provided that the prime 2 splits neither in K/Q nor in Q(root-m)/Q, in terms of a congruence satisfied by the value of a 2-adic L-function for K at 1. (C) 1997 Academic Press.

[发布日期] 1997-12-01