Timeline for A strange condition on containment of special complex numbers in cyclotomic fields

9 events

when toggle format	what		by	license	comment
Apr 1, 2015 at 19:19	answer	added	Sent from my iphone		timeline score: -1
S Mar 30, 2015 at 19:02	history	suggested	Robert A. Neiss	CC BY-SA 3.0	Restrict $a$ to roots of unity.
Mar 30, 2015 at 18:55	review	Suggested edits
S Mar 30, 2015 at 19:02
S Mar 30, 2015 at 18:46	history	suggested	Robert A. Neiss	CC BY-SA 3.0	Restrict $a$ to roots of unity.
Mar 30, 2015 at 18:36	review	Suggested edits
S Mar 30, 2015 at 18:46
Mar 30, 2015 at 15:32	comment	added	David Loeffler		(PS: I suspect this isn't an answer to the question you meant to ask, so can you refine the question to rule out such silliness?)
Mar 30, 2015 at 15:30	comment	added	David Loeffler		You want this to be impossible for $a \in \mathbf{C}^*$ and $\|a\| < 1/4$, with no other conditions on $a$? Then you're out of luck. Let $\rho$ be a rational number a tiny little bit bigger than 1/2 (but smaller than $\sqrt{1/4 + 1/4^m}$). Then there's a unique real algebraic number $a \in (0, 1/4)$ such that $\sqrt{1/4 + a^m} = \rho$, and for this $a$ the condition that $\sqrt{1/4 + a^m} \in \mathbf{Q}(\zeta_m, a)$ is vacuously satisfied because $\rho \in \mathbf{Q}$.
Mar 30, 2015 at 14:00	review	First posts
Mar 30, 2015 at 14:03
Mar 30, 2015 at 13:59	history	asked	Robert A. Neiss	CC BY-SA 3.0