Hi! If a holomorphic function ##f:G \to C##, where ##G## is a region in the complex plane is equal to zero for all values ##z## in a disk ##D_{[z_0,r]}##, inside ##G##, is it zero everywhere in the region G? And if this is true, does it mean that if an entire function is zero in a disk, it is zero in the whole complex plane? Thank you!(adsbygoogle = window.adsbygoogle || []).push({});

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# I Identical zero function in the complex plane

Have something to add?

Draft saved
Draft deleted

Loading...

Similar Threads for Identical zero function |
---|

I Does the Integral of Riemman Zeta Function have a meaning? |

I Question about inverse function |

I Elementary question on composition of functions |

I Distributions (generalised functions) basics |

I Impossible to lift the identity map on the circle |

**Physics Forums | Science Articles, Homework Help, Discussion**