Nonpolar singularities of local zeta functions in some smooth case

Kamimoto, Joe; Nose, Toshihiro

doi:10.1090/tran/7771

Nonpolar singularities of local zeta functions in some smooth case
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by Joe Kamimoto and Toshihiro Nose PDF

Trans. Amer. Math. Soc. 372 (2019), 661-676 Request permission

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.

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