If $f$ is a holomorphic function defined on an open and connected set, and the set of zeros of $f$ has a cluster point/accumulation point/limit point then it is identically $0$.
I can't think of a way to proceed. Any hints are appreciated
2026-03-28 21:27:09.1774733229
If the set of roots has cluster point then function is identically zero
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What you stated is a particular case of the identity theorem.