most recent 30 from http://mathoverflow.net 2013-05-21T12:49:30Z http://mathoverflow.net/feeds/question/79898 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/79898/zeros-of-a-holomorphic-function-in-several-variable spr 2011-11-03T06:12:35Z 2011-11-03T08:42:26Z

<p>Let $f$ be a holomorphic function in $n$ complex variables on a domain $D\subset \mathbb C^n$. Let $S$ be a subset of $D$ such that for a polynomial $P$ in $n$ variable, $P(S)=(a,b)$ for an interval $(a,b)$. Can $f$ be zero on $S$? </p> <p>What happens if $P(S)=(a,b)\cap \mathbb Q$?</p>