1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: A graduate level question in complex analysis

  1. Jul 24, 2008 #1
    If f and g are two entire functions such that mod(f(z)) <= mod(g(z)) for all z in C, prove that f=cg for some complex constant c.
     
  2. jcsd
  3. Jul 24, 2008 #2
    I tried to prove this by applying Liouville's theorem to f/g.
    it is clear that f/g is bounded.
    and f/g is analytic except at the zeros of g.
    if z1 is a zero of g its a zero of f also.
    and if multiplicity of z1 as a zero of g will be less than or equal to multiplicity of z1 as a zero of f.
    i got stuck here.
    pls help me to prove f/g is analytic at zeros of g also.
    so that by Liouville's theorem f/g will be a constant.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook