Sharp Remez inequality

S. Tikhonov, P. Yuditskii

Let an algebraic polynomial $P_n(\zeta )$ of degree $n$ be such that $|P_n(\zeta )|\le 1$ for $\zeta \in E\subset \mathbb{T}$ and $|E|\ge 2\pi -s$. We prove the sharp Remez inequality $$ \sup_{ζ\in\m…