My Math Forum bounded domain, meromorphic functions

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 January 17th, 2010, 11:34 AM #1 Newbie   Joined: Mar 2009 Posts: 28 Thanks: 0 bounded domain, meromorphic functions Let $D$ be a bounded domain, and let $f(z)$ and $h(z)$ be meromorphic functions on $D$ that extend to be analytic on $\partial D$. Suppose that $|h(z)|< |f(z)|$ on $\partial D$. Show by example that $f(z)$ and $f(z)+h(z)$ can have different numbers of zeros on $D$. What can be said about $f(z)$ and $f(z)+h(z)$? Prove your assertion. I do not see what example I can use here. I think what we can say is that they have the same number of zeros minus poles. I just don't see an example here. Thanks.

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