T-symmetric Koebe radius conjecture for schlicht polynomials

From papers

Let TT and NN be positive integers, and let F(0)F^{(0)} be the polynomial proposed as the extremizer for the TT-symmetric univalent-polynomial optimization problem. A schlicht polynomial is a univalent polynomial on D={z:z<1}\mathbb D=\{z:|z|<1\} with the stated TT-fold symmetry and degree NN. T-symmetric Koebe radius conjecture. The image of D\mathbb D under every TT-symmetric schlicht polynomial of degree NN contains a disc of radius

F(0)(eiπT),\left|F^{(0)}\left(e^{\frac{i\pi}{T}}\right)\right|,

and this value is sharp. This is presented as a polynomial analogue of the TT-symmetric Koebe theorem; the source gives no proof or resolution status.

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Sources & referencesView supporting material

Primary source

Dmitriy Dmitrishin, Daniel Gray, Alexander Stokolos and Iryna Tarasenko, “An extremal problem for odd univalent polynomials”, arXiv:2208.02054 (2022).

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