hw13-201141 - | f ( z ) | = | g ( z ) | for all | z |...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Homework 13. (1) Let G be open and connected and f,g analytic on G such that f ( z ) g ( z ) = 0 for all z G . Prove that either f ( z ) = 0 for all z G or g ( z ) = 0 for all z G . (2) (Quals ’02) Let f,g : { z : | z | < 1 } → C be analytic functions such that
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: | f ( z ) | = | g ( z ) | for all | z | &lt; 1. Prove that every zero of g is also a zero of f of the same multiplicity and that thus f = g for some with modulus one. 1...
View Full Document

Ask a homework question - tutors are online