On the number of solutions of an algebraic equation on the curve <IMG ALIGN=MIDDLE HEIGHT=28 WIDTH=178>, and a consequence for o-minimal structures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

On the number of solutions of an algebraic equation on the curve , and a consequence for o-minimal structures

Authors:	Janusz Gwozdziewicz Krzysztof Kurdyka Adam Parusinski

Affiliation:	Department of Mathematics, Technical University, Al.~1000LPP7, 25--314~Kielce, Poland ; Laboratoire de Mathématiques, Université de Savoie, Campus Scientifique 73 376 Le Bourget--du--Lac Cedex, France and Instytut Matematyki, Uniwersytet Jagiellonski, ul. Reymonta 4 30--059 Kraków, Poland ; Département de Mathématiques, Université d'Angers, 2, bd Lavoisier, 49045 Angers cedex 01, France

Abstract:	We prove that every polynomial of degree has at most $2(d+2)^{12}$ zeros on the curve $y=e^{x}+\sin (x),\quad x>0$ . 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.

Keywords:	Fewnomial Khovansky theory o-minimal structure

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