an:01245430
Zbl 0916.03026
Gwozdziewicz, Janusz; Kurdyka, Krzysztof; Parusinski, Adam
On the number of solutions of an algebraic equation on the curve \(y = e^{x} +\sin x, x>0\), and a consequence for o-minimal structures
EN
Proc. Am. Math. Soc. 127, No. 4, 1057-1064 (1999).
00054319
1999
j
03C50 14P15 26E05
algebraic equation; fewnomial; Khovansky theory; o-minimal structure; analytic curve
It is proved that every polynomial \(P(x,y)\) of degree \(d\) has at most \(2(d+ 2)^{12}\) zeros on the curve \(y= e^x+ \sin(x)\), \(x>0\).
As a consequence the authors obtain 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.
Viorel V??j??itu (Bucure??ti)