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

Thanks.

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- August 30th 2011, 01:29 AMVeveanalytic function on open annulus
If f is a non-zero analytic function on the open annulus A= {z in ; 1<|z|<2}, how can I prove that there exists an integer m such that for all r . 1<r<2, 1/ i _{|z|=r} f '(z)/f(z) dz =m ?

Thanks. - August 30th 2011, 02:09 AMchisigmaRe: analytic function on open annulus
A proof of the 'argument principle theorem' is here...

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

Kind regards