A number field extension of a question of Milnor

Milnor formulated a conjecture about rational linear independence of some special Hurwitz zeta values. The second and third authors along with Ram Murty studied this conjecture and suggested an extension of Milnor's conjecture. In this note, we investigate the number field generalisation of this extended Milnor conjecture. We indicate the motivation for considering this number field case by noting that such a phenomenon is true in an analogous context. We also study some new spaces related to normalised Hurwitz zeta values.