Timeline for Why do roots of polynomials tend to have absolute value close to 1?

9 events

when toggle format	what		by	license	comment
Oct 9, 2014 at 15:48	comment	added	asmeurer		I think one would need to show that random polynomials tend to be near-cyclotomic.
Oct 7, 2014 at 0:29	comment	added	François G. Dorais		As seen in my answer, this doesn't seem to explain rotational symmetry at all. In fact, it suggests the opposite.
Oct 6, 2014 at 14:32	comment	added	Martin Brandenburg		"Then the ai's will be roughly equal," Why?
Oct 6, 2014 at 13:49	history	edited	tros443	CC BY-SA 3.0	added 128 characters in body
Oct 5, 2014 at 16:21	comment	added	Joonas Ilmavirta		Continuity only seems to explain it for small perturbations of the coefficients. I know that this is only supposed to be a heuristic justification, so it is not an enormous issue.
Oct 5, 2014 at 15:53	comment	added	tros443		Well, the roots of a polynomial as a function of its coefficient is a continuous function. So polynomials with coefficients that are roughly equal, have roots that are roughly equal.
Oct 5, 2014 at 15:38	comment	added	Joonas Ilmavirta		This is a nice intuitive explanation, but there is a gap that I have hard time filling heuristically. It is not at all clear that if the coefficients of a polynomial are equal on average, their zeroes should be where they were if the coefficients were actually equal. Is there a simple explanation for this?
Oct 5, 2014 at 15:28	review	First posts
Oct 5, 2014 at 15:38
Oct 5, 2014 at 15:23	history	answered	tros443	CC BY-SA 3.0