论文标题
在某些平滑情况下
Meromorphic continuation and non-polar singularities of local zeta functions in some smooth cases
论文作者
论文摘要
众所周知，与实际分析函数相关的局部ZETA函数可以在孔复合平面上作为Meromormormorphic函数进行分析。在本文中，精确研究了某些特定（非现实分析）平滑功能的情况。特别是，我们在一个方向上给出了某些奇异性的局部Zeta函数的渐近极限。从这些局部ZETA函数具有与极点不同的奇异性的行为来看。然后，我们显示了一定数量较低估计值的最佳性，与元素Zeta函数的meromorphic延续有关，以所有平滑函数表示为$ u（x，x，y）x^a y^b +$ flat flat fluct函数，其中$ u（0,0,0）\ neq 0 $和$ a，b $ b $是非对整体的notegative integers and n n n n n notegative Integers满意$ aq $ aq $ aq b $ \ neq b $ \ neq b $ \ neq b $ \ neq b。
It is known that local zeta functions associated with real analytic functions can be analytically continued as meromorphic functions to the hole 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 the behaviors that these 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 the case of all smooth functions expressed as $u(x,y)x^a y^b +$ flat function, where $u(0,0)\neq 0$ and $a,b$ are nonnegative integers satisfying $a\neq b$.
