Meromorphic continuation and non-polar singularities of local zeta functions in some smooth cases
Year: 2025
Type: article
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, certain cases of specific (non-real analytic) smooth functions are precisely investigated. In particular, we give asymptotic limits of local zeta functions at some singularities along one direction. It follows from these behaviors that the respective local zeta functions have singularities different from poles. Then we show the optimality of the lower estimates of a certain quantity concerning with meromorphic continuation of local zeta functions in some smooth model cases.
Source: Tohoku Mathematical Journal
DOI: 10.2748/tmj.20231107
Author: Toshihiro Nose
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4413764136