Some problem of complex multi-function











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Assume that $f:Urightarrow mathbb{C}$ is a holomorphic function on a connected open subset of $mathbb{C}^n$.



Then can we prove that for every point $xin U$. There would be a local coordinates $(z_1,...,z_n)$ around $x$ such that $f=z_1z_2cdots z_n$?






complex-analysis complex-geometry several-complex-variables







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    down vote

    favorite












    Assume that $f:Urightarrow mathbb{C}$ is a holomorphic function on a connected open subset of $mathbb{C}^n$.



    Then can we prove that for every point $xin U$. There would be a local coordinates $(z_1,...,z_n)$ around $x$ such that $f=z_1z_2cdots z_n$?






    complex-analysis complex-geometry several-complex-variables







    share|cite|improve this question


























      up vote
      0
      down vote

      favorite









      up vote
      0
      down vote

      favorite











      Assume that $f:Urightarrow mathbb{C}$ is a holomorphic function on a connected open subset of $mathbb{C}^n$.



      Then can we prove that for every point $xin U$. There would be a local coordinates $(z_1,...,z_n)$ around $x$ such that $f=z_1z_2cdots z_n$?






      complex-analysis complex-geometry several-complex-variables







      share|cite|improve this question















      Assume that $f:Urightarrow mathbb{C}$ is a holomorphic function on a connected open subset of $mathbb{C}^n$.



      Then can we prove that for every point $xin U$. There would be a local coordinates $(z_1,...,z_n)$ around $x$ such that $f=z_1z_2cdots z_n$?






      complex-analysis complex-geometry several-complex-variables




      complex-analysis complex-geometry several-complex-variables






      share|cite|improve this question















      share|cite|improve this question













      share|cite|improve this question




      share|cite|improve this question








      edited yesterday









      Kenny Wong

      16.6k21135




      16.6k21135










      asked yesterday









      Intoks Liobein

      41128




      41128



























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