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Sep 5, 2012 at 15:15 comment added user2013 @Peter, I misunderstood your answer. You are totally right.
Sep 5, 2012 at 7:29 comment added Peter Mueller @Muon: Not sure what the problem is: By $g^\sigma$ I mean the field automorphism $\sigma$ applied to the coefficients of $g$. So if one coefficient of $g$ is $1$, then applying $\sigma$ doesn't change this coefficient. So if $g^\sigma$ is a scalar multiple of $g$, we must have $g^\sigma=g$.
Sep 4, 2012 at 19:16 comment added user2013 How do you conclude that $\mu=1$ for any $\sigma \in \mathrm{Aut}(\mathbb{C})$
Sep 4, 2012 at 9:26 history answered Peter Mueller CC BY-SA 3.0