Interior zero count for a finite Blaschke product minus a constant
= Interior zero count for a finite Blaschke product minus a constant
{title2=$N(B-a)=\deg B\quad(|a|<1)$}
A finite <Blaschke product> is holomorphic across the unit circle and has modulus one there. For a constant $a$ with $|a|<1$, <Rouché's theorem> makes $B-a$ and $B$ have the same number of interior zeros, counting <multiplicity>. Each factor contributes its prescribed zero; the poles are outside the closed disk.