Chebyshev constants for the unit circle

Gergely Ambrus, Keith M. Ball, T. Erdélyi

It is proven that for any system of n points z_1, ..., z_n on the (complex) unit circle, there exists another point z of norm 1, such that $$\sum 1/|z-z_k{|}^2\le n^2/4.$$ Equality…