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 cn, where c\equal{}c(M) >0 is a constant depending only on M.
G. Halasz algebrapolynomialadvanced fieldsadvanced fields unsolved