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Math Help - analytic function on open annulus

  1. #1
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    analytic function on open annulus

    If f is a non-zero analytic function on the open annulus A= {z in \mathbb{C}; 1<|z|<2}, how can I prove that there exists an integer m such that for all r . 1<r<2, 1/ 2\pii \int_{|z|=r} f '(z)/f(z) dz =m ?

    Thanks.
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  2. #2
    MHF Contributor chisigma's Avatar
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    Re: analytic function on open annulus

    Quote Originally Posted by Veve View Post
    If f is a non-zero analytic function on the open annulus A= {z in \mathbb{C}; 1<|z|<2}, how can I prove that there exists an integer m such that for all r . 1<r<2, 1/ 2\pii \int_{|z|=r} f '(z)/f(z) dz =m ?

    Thanks.
    A proof of the 'argument principle theorem' is here...

    http://www.joensuu.fi/matematiikka/k...plex/luku3.pdf

    Kind regards

    \chi \sigma
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