A multiquadratic field generalization of Artin's conjecture

We prove (under the assumption of the generalized Riemann hypothesis) that a totally real multiquadratic number field K has a positive density of primes p   in ZZ for which the image of OK× in (OK/pOK)×(OK/pOK)× has minimal index (p−1)/2(p−1)/2 if and only if K   contains a unit of norm −1. An explicit formula for this density is provided. We also discuss an application to ray class fields of conductor pOKpOK.