Abstract
LetK=Q(m) be a real quadratic number field. In this article, we find a necessary and sufficient condition forKto admit an unramified quadratic extension with a normal integral basis distinct fromK(1), provided that the prime 2 splits neither inK/Q nor in Q(−m)/Q, in terms of a congruence satisfied by the value of a 2-adicL-function forKat 1.
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