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Nov 1, 2023 at 19:00 comment added GH from MO The "Close" votes are not justified. Please do not vote to close this question, as it is clearly on topic.
Oct 30, 2023 at 19:14 comment added fedja The trivial lower bound is $\frac\pi 2M$. It is certainly not sharp and will improve to the desired bound $2M$ if we could show, for instance, that for every polynomial $P$ with the roots on the circle and maximal value $2$, we have $|\{|P|>t\}|\le|\{|z-1|>t\}|$ for all $t\in(0,2)$, which seems plausible but I have no proof at the moment :-).
Oct 29, 2023 at 10:30 vote accept user159888
Oct 29, 2023 at 1:03 comment added LSpice @‍Conrad's answer referenced by @GHfromMO, and their comment on it.
Oct 29, 2023 at 1:02 history edited LSpice CC BY-SA 4.0
Tidying, while this is on the front page
Oct 29, 2023 at 0:56 comment added GH from MO See my comment to Conrad's post below.
Oct 28, 2023 at 23:48 answer added Conrad timeline score: 9
Oct 28, 2023 at 14:30 history became hot network question
Oct 28, 2023 at 9:58 comment added user159888 Sorry, there was a typo. corrected it now.
Oct 28, 2023 at 9:57 history edited user159888 CC BY-SA 4.0
edited body
Oct 28, 2023 at 9:39 answer added Oscar Lanzi timeline score: 1
Oct 28, 2023 at 7:57 review Close votes
Nov 4, 2023 at 3:04
Oct 28, 2023 at 6:42 comment added Fedor Petrov What about $1+z+... +z^n$?
Oct 28, 2023 at 6:29 history asked user159888 CC BY-SA 4.0