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: Elliptic functions proof f(z)-c has N zeros, N the order

  1. Jun 28, 2017 #1
    1. The problem statement, all variables and given/known data

    proof of theorem

    2. Relevant equations

    3. The attempt at a solution

    I have a couple of questions on the attached proof and theorem

    1) On the last line, how is it we go from the order of the zeros = the number of zeros, or is it's meaning the number of zeros counted with multiplicity. - Am I correct in thinking that:

    order of pole/zero = number of poles/zeros * multiplicity at each point ?

    2) The zero expansion considered is fine since we are considering zeros of ##f(z)-c##. But for expansion about a pole of ##f(z)##, near that pole, how is it we can say that that same expansion holds for ##f(z)-c##? Is this not making some assumptions on ##c## being small?

    Many thank in advance.
  2. jcsd
  3. Jul 3, 2017 #2
    Thanks for the thread! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post? The more details the better.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted