The theorems of Schottky and Landau for analytic functions omitting the   n-th roots of unity
  We prove sharp Landau- and Schottky-type theorems for analytic functions which omit the $n$-th roots of unity. The proofs are based on a sharp lower bound for the Poincar\'e metric of the complex plane punctured at the roots of unity. 
Daniela Kraus, Oliver Roth
math.CV