If holomorphic f_n converge locally uniformly to a non-zero limit f on Ω and f has a zero of order k at z_0, then for n large f_n has exactly k zeros (counted with multiplicity) in any sufficiently small disk around z_0. Corollary:…
If holomorphic f_n converge locally uniformly to a non-zero limit f on Ω and f has a zero of order k at z_0, then for n large f_n has exactly k zeros (counted with multiplicity) in any sufficiently small disk around z_0. Corollary:…