Non-polar singularities of local zeta functions in some smooth case

Joe Kamimoto; Toshihiro Nose

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arXiv · 1803.10029

Non-polar singularities of local zeta functions in some smooth case

Joe Kamimoto·Toshihiro Nose

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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 (non-real 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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Joe Kamimoto, Toshihiro Nose. 2018-03-27. Non-polar singularities of local zeta functions in some smooth case. https://arxiv.org/abs/1803.10029

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