A number field extension of a question of Milnor

TL;DR

This paper explores a generalization of Milnor's conjecture on Hurwitz zeta values within number fields, motivated by analogous phenomena and involving new spaces related to normalized Hurwitz zeta values.

Contribution

It investigates the number field extension of an extended Milnor conjecture and introduces new spaces connected to normalized Hurwitz zeta values.

Findings

The number field generalization aligns with analogous phenomena.

New spaces related to normalized Hurwitz zeta values are studied.

Motivates further research in number field contexts.

Abstract

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.