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Complex Analysis and Geometry pp 187–195Cite as

On Meromorphic Continuation of Local Zeta Functions

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Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 144))

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.

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Author information

Authors and Affiliations

  1. Faculty of Mathematics, Kyushu University, Motooka 744, Nishi-ku, Fukuoka, 819-0395, Japan

    Joe Kamimoto

  2. Faculty of Engineering, Kyushu Sangyo University, Matsukadai 2-3-1, Higashi-ku, Fukuoka, 813-8503, Japan

    Toshihiro Nose

Authors
  1. Joe Kamimoto
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  2. Toshihiro Nose
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Corresponding author

Correspondence to Toshihiro Nose .

Editor information

Editors and Affiliations

  1. Department of Mathematics, Università di Roma Tor Vergata, Rome, Italy

    Filippo Bracci

  2. Dept. of Mathematics Education, Kyungnam University, Changwon, Korea (Republic of)

    Jisoo Byun

  3. Université Joseph Fourier Grenoble, Institut Fourier, Grenoble, France

    Hervé Gaussier

  4. Graduate School of Mathematical Sciences, The University of Tokyo, Meguro-ku, Tokyo, Japan

    Kengo Hirachi

  5. Department of Mathematics, POSTECH, Pohang, Korea (Republic of)

    Kang-Tae Kim

  6. Department of Mathematics, Bergische Universität Wuppertal, Wuppertal, Nordrhein-Westfalen, Germany

    Nikolay Shcherbina

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Kamimoto, J., Nose, T. (2015). On Meromorphic Continuation of Local Zeta Functions. In: Bracci, F., Byun, J., Gaussier, H., Hirachi, K., Kim, KT., Shcherbina, N. (eds) Complex Analysis and Geometry. Springer Proceedings in Mathematics & Statistics, vol 144. Springer, Tokyo. https://doi.org/10.1007/978-4-431-55744-9_13

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