Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4593118 | Journal of Number Theory | 2017 | 28 Pages |
Abstract
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.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
M.E. Stadnik,