Newton polygons and local integrability of negative powers of smooth functions in the plane期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Newton polygons and local integrability of negative powers of smooth functions in the plane

Authors:	Michael Greenblatt

Institution:	Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139

Abstract:	Let be any smooth real-valued function with . For a sufficiently small neighborhood of the origin, we study the number $\begin{displaymath}\sup\left\{\epsilon:\int_U \vert f(x,y)\vert^{-\epsilon}<\infty\right\}. \end{displaymath}$ It is known that sometimes this number can be expressed in a natural way using the Newton polygon of . We provide necessary and sufficient conditions for this Newton polygon characterization to hold. The behavior of the integral at the supremal $\epsilon$ is also analyzed.

Keywords:	Resolution of singularities Newton polygon

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