Unramified Quadratic Extensions of Real Quadratic Fields, Normal Integral Bases, and 2-AdicL-Functions Original Research Article

LetK=image(image) 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(image), provided that the prime 2 splits neither inK/image nor in image(image)/image, in terms of a congruence satisfied by the value of a 2-adicL-function forKat 1.