Nonpolar singularities of local zeta functions in some smooth case

Joe Kamimoto, Toshihiro Nose

    Research output: Contribution to journalArticlepeer-review

    4 Citations (Scopus)

    Abstract

    It is known that local zeta functions associated with real analytic functions can be analytically continued as meromorphic functions to the whole complex plane. In this paper, the case of specific (nonreal analytic) smooth functions is precisely investigated. Indeed, asymptotic limits of the respective local zeta functions at some singularities in one direction are explicitly computed. Surprisingly, it follows from these behaviors that these local zeta functions have singularities different from poles.

    Original languageEnglish
    Pages (from-to)661-676
    Number of pages16
    JournalTransactions of the American Mathematical Society
    Volume372
    Issue number1
    DOIs
    Publication statusPublished - 2019

    All Science Journal Classification (ASJC) codes

    • General Mathematics
    • Applied Mathematics

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