# Chebyshev constants for the unit circle - Mathematics > Metric Geometry

Chebyshev constants for the unit circle - Mathematics > Metric Geometry - Download this document for free, or read online. Document in PDF available to download.

Abstract: It is proven that for any system of n points z 1,

., z n on the complexunit circle, there exists another point z of norm 1, such that$$\sum 1-|z-z k|^2 \leq n^2-4.$$ Equality holds iff the point system is arotated copy of the nth unit roots.Two proofs are presented: one uses a characterisation of equioscillatingrational functions, while the other is based on Bernstein-s inequality.

Author: ** Gergely Ambrus, Keith M. Ball, T. Erdélyi**

Source: https://arxiv.org/