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ON THE POLES OF MAXIMAL ORDER OF THE TOPOLOGICAL ZETA FUNCTION

Published online by Cambridge University Press:  01 July 1999

ANN LAEREMANS  and
WILLEM VEYS
ANN LAEREMANS
Affiliation:
EHSAL, Stormstraat 2, B–1000 Brussels, Belgium
WILLEM VEYS
Affiliation:
Departement Wiskunde, Celestijnenlaan 200B, B–3001 Leuven, Belgium
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Abstract

The global and local topological zeta functions are singularity invariants associated to a polynomial f and its germ at 0, respectively. By definition, these zeta functions are rational functions in one variable, and their poles are negative rational numbers. In this paper we study their poles of maximal possible order. When f is non-degenerate with respect to its Newton polyhedron, we prove that its local topological zeta function has at most one such pole, in which case it is also the largest pole; we give a similar result concerning the global zeta function. Moreover, for any f we show that poles of maximal possible order are always of the form −1/N with N a positive integer.

Type
NOTES AND PAPERS
Information
Bulletin of the London Mathematical Society , Volume 31 , Issue 4 , July 1999 , pp. 441 - 449
Copyright
© The London Mathematical Society 1999

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