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

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

Authors:	Michael Greenblatt

Affiliation:	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 $begin{displaymath}supleft{epsilon:int_U vert f(x,y)vert^{-epsilon}<inftyright}. end{displaymath}$ 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 is also analyzed.

Keywords:	Resolution of singularities Newton polygon

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