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Question about Riemann Surface Problem

  1. Feb 14, 2016 #1
    1. The problem statement, all variables and given/known data
    [tex] f(z)=z^\frac{3}{2} [/tex] find the branch points, branch cuts, and Riemann sheet structure.
    2. Relevant equations
    none

    3. The attempt at a solution
    So, I converted this to complex exponential form [tex] r^\frac{3}{2} e^\frac{i*3*\Theta}{2} [/tex] From here I mapped around a circle that was centered about the orgin. After cycling through 2 Pi I could see that z mapped into f(z) and wasn't at it's original point. So I concluded the branch points were at the origin and infinity (I think infinity is a branch point because z^-3/2 goes to 0 as z goes to infinity.

    I think the cut can go from the origin to infinity in any direction.

    The Riemann surfaces is giving me the most trouble. I keep going back and forth between this function being multivalued or not.

    Thanks for any help!
     
  2. jcsd
  3. Feb 19, 2016 #2
    Thanks for the post! 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?
     
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