### Abstract

We investigate meromorphic continuation of local zeta functions and properties of their poles. In the real analytic case, local zeta functions can be meromorphically continued to the whole complex plane and, moreover, properties of the poles have been precisely investigated. However, in the only smooth case, the situation of meromorphic continuation is very different. Actually, there exists an example in which a local zeta function has a singularity different from poles. We give a sufficient condition for that the first finitely many poles samely appear as in the real analytic case and exactly investigate properties of the first pole.

Original language | English |
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Title of host publication | Complex Analysis and Geometry - KSCV 2014 |

Editors | Jisoo Byun, Filippo Bracci, Hervé Gaussier, Kang-Tae Kim, Nikolay Shcherbina, Kengo Hirachi |

Publisher | Springer New York LLC |

Pages | 187-195 |

Number of pages | 9 |

ISBN (Print) | 9784431557432 |

DOIs | |

Publication status | Published - Jan 1 2015 |

Event | 10th Korean Conference on Several Complex Variables, KSCV 2014 - Gyeongju, Korea, Republic of Duration: Aug 7 2014 → Aug 11 2014 |

### Publication series

Name | Springer Proceedings in Mathematics and Statistics |
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Volume | 144 |

ISSN (Print) | 2194-1009 |

ISSN (Electronic) | 2194-1017 |

### Other

Other | 10th Korean Conference on Several Complex Variables, KSCV 2014 |
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Country | Korea, Republic of |

City | Gyeongju |

Period | 8/7/14 → 8/11/14 |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)

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## Cite this

*Complex Analysis and Geometry - KSCV 2014*(pp. 187-195). (Springer Proceedings in Mathematics and Statistics; Vol. 144). Springer New York LLC. https://doi.org/10.1007/978-4-431-55744-9_13