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Motivic invariants of real polynomial functions and their Newton polyhedrons

Published online by Cambridge University Press:  26 November 2015

GOULWEN FICHOU  and
TOSHIZUMI FUKUI
GOULWEN FICHOU
Affiliation:
IRMAR (UMR 6625), Université de Rennes 1, Campus de Beaulieu, 35042 Rennes Cedex, France. e-mail: goulwen.fichou@uni-renns1.fr
TOSHIZUMI FUKUI
Affiliation:
Department of Mathematics, Faculty of Science, Saitama University, Saitama, 338-8570, Japan. e-mail: tfukui@rimath.saitama-u.ac.jp
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Abstract

We give an expression of the motivic zeta function for a real polynomial function in terms of the Newton polyhedron of the function. As a consequence, we show that the weights are determined by the motivic zeta function for convenient weighted homogeneous polynomials in three variables. We apply this result to the blow-Nash equivalence.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 160 , Issue 1 , January 2016 , pp. 141 - 166
Copyright
Copyright © Cambridge Philosophical Society 2015 

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