On meromorphic continuation of local zeta functions

Joe Kamimoto, Toshihiro Nose

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    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 languageEnglish
    Title of host publicationComplex Analysis and Geometry - KSCV 2014
    EditorsJisoo Byun, Filippo Bracci, Hervé Gaussier, Kang-Tae Kim, Nikolay Shcherbina, Kengo Hirachi
    PublisherSpringer New York LLC
    Pages187-195
    Number of pages9
    ISBN (Print)9784431557432
    DOIs
    Publication statusPublished - 2015
    Event10th Korean Conference on Several Complex Variables, KSCV 2014 - Gyeongju, Korea, Republic of
    Duration: Aug 7 2014Aug 11 2014

    Publication series

    NameSpringer Proceedings in Mathematics and Statistics
    Volume144
    ISSN (Print)2194-1009
    ISSN (Electronic)2194-1017

    Other

    Other10th Korean Conference on Several Complex Variables, KSCV 2014
    Country/TerritoryKorea, Republic of
    CityGyeongju
    Period8/7/148/11/14

    All Science Journal Classification (ASJC) codes

    • General Mathematics

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