Nonpolar singularities of local zeta functions in some smooth case
Nonpolar singularities of local zeta functions in some smooth case
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某些光滑情况下局部 zeta 函数的非极性奇点
DOI：
10.1090/tran/7771
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发表时间：
2019
影响因子：
1.3
通讯作者：
Nose Toshihiro
中科院分区：
文献类型：
--
作者：
Kamimoto Joe;Nose Toshihiro
已知与实解析函数相关的局部Zeta函数可以解析地连续为整个复平面上的亚纯函数。本文对特殊的(非实解析)光滑函数的情形进行了细致的研究。实际上，各个局部Zeta函数在一个方向上的某些奇点处的渐近极限被显式地计算出来。令人惊讶的是，从这些行为可以得出，这些局部Zeta函数具有与极点不同的奇点。参考文献
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. References