### 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 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### 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

**On meromorphic continuation of local zeta functions.** / Kamimoto, Joe; Nose, Toshihiro.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Complex Analysis and Geometry - KSCV 2014.*Springer Proceedings in Mathematics and Statistics, vol. 144, Springer New York LLC, pp. 187-195, 10th Korean Conference on Several Complex Variables, KSCV 2014, Gyeongju, Korea, Republic of, 8/7/14. https://doi.org/10.1007/978-4-431-55744-9_13

}

TY - GEN

T1 - On meromorphic continuation of local zeta functions

AU - Kamimoto, Joe

AU - Nose, Toshihiro

PY - 2015/1/1

Y1 - 2015/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84950985930&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84950985930&partnerID=8YFLogxK

U2 - 10.1007/978-4-431-55744-9_13

DO - 10.1007/978-4-431-55744-9_13

M3 - Conference contribution

AN - SCOPUS:84950985930

SN - 9784431557432

T3 - Springer Proceedings in Mathematics and Statistics

SP - 187

EP - 195

BT - Complex Analysis and Geometry - KSCV 2014

A2 - Byun, Jisoo

A2 - Bracci, Filippo

A2 - Gaussier, Hervé

A2 - Kim, Kang-Tae

A2 - Shcherbina, Nikolay

A2 - Hirachi, Kengo

PB - Springer New York LLC

ER -