MathDB

Let

P(z)

be a polynomial of degree

n

with complex coefficients, P(0)\equal{}1, \;\textrm{and}\ \;|P(z)|\leq M\ \;\textrm{for}\ \;|z| \leq 1\ . Prove that every root of

P(z)

in the closed unit disc has multiplicity at most

c\sqrt{n}

, where c\equal{}c(M) >0 is a constant depending only on

M

. G. Halasz

Problem Statement