On the number of solutions of an algebraic equation on the curve ,

and a consequence for o-minimal structures

Authors:
Janusz Gwozdziewicz, Krzysztof Kurdyka and Adam Parusinski

Journal:
Proc. Amer. Math. Soc. **127** (1999), 1057-1064

MSC (1991):
Primary 32B20, 32C05, 14P15; Secondary 26E05, 03C99

DOI:
https://doi.org/10.1090/S0002-9939-99-04672-9

MathSciNet review:
1476134

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Abstract | References | Similar Articles | Additional Information

Abstract: We prove that every polynomial of degree has at most zeros on the curve . As a consequence we deduce that the existence of a uniform bound for the number of zeros of polynomials of a fixed degree on an analytic curve does not imply that this curve belongs to an o-minimal structure.

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Additional Information

**Janusz Gwozdziewicz**

Affiliation:
Department of Mathematics, Technical University, Al. 1000LPP7, 25–314 Kielce, Poland

Email:
matjg@eden.tu.kielce.pl

**Krzysztof Kurdyka**

Affiliation:
Laboratoire de Mathématiques, Université de Savoie, Campus Scientifique 73 376 Le Bourget–du–Lac Cedex, France and Instytut Matematyki, Uniwersytet Jagielloński, ul. Reymonta 4 30–059 Kraków, Poland

Email:
Krzysztof.Kurdyka@univ-savoie.fr

**Adam Parusinski**

Affiliation:
Département de Mathématiques, Université d’Angers, 2, bd Lavoisier, 49045 Angers cedex 01, France

Email:
parus@tonton.univ-angers.fr

DOI:
https://doi.org/10.1090/S0002-9939-99-04672-9

Keywords:
Fewnomial,
Khovansky theory,
o-minimal structure

Received by editor(s):
July 15, 1997

Communicated by:
Steven R. Bell

Article copyright:
© Copyright 1999
American Mathematical Society