The eigenspaces of twisted polynomials over cyclic field extensions

Abstract

Let $K$ be a field and $\sigma$ an automorphism of $K$ of order $n$. We study the eigenspace of a bounded skew polynomial $f\in K[t;\sigma]$, with emphasis on the case of a cyclic field extension $K/F$ of degree $n$, where $\sigma$ generates the Galois group. We obtain lower bounds on its dimension, and compute it in special cases.Comment: Rewritten and streamlined new version, some results are improve