This paper is concerned with the density of rational points on the graph of a non-algebraic pfaffian function.
Cet article est concerné par la densité de points rationnels sur le graphe d’une fonction pfaffienne non-algébrique.
@article{AFST_2007_6_16_3_635_0,
author = {Pila, Jonathan},
title = {The density of rational points on a pfaff curve},
journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
pages = {635--645},
publisher = {Universit\'e Paul Sabatier, Institut de math\'ematiques},
address = {Toulouse},
volume = {Ser. 6, 16},
number = {3},
year = {2007},
doi = {10.5802/afst.1162},
mrnumber = {2379055},
language = {en},
url = {http://archive.numdam.org/articles/10.5802/afst.1162/}
}
TY - JOUR AU - Pila, Jonathan TI - The density of rational points on a pfaff curve JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 2007 SP - 635 EP - 645 VL - 16 IS - 3 PB - Université Paul Sabatier, Institut de mathématiques PP - Toulouse UR - http://archive.numdam.org/articles/10.5802/afst.1162/ DO - 10.5802/afst.1162 LA - en ID - AFST_2007_6_16_3_635_0 ER -
%0 Journal Article %A Pila, Jonathan %T The density of rational points on a pfaff curve %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2007 %P 635-645 %V 16 %N 3 %I Université Paul Sabatier, Institut de mathématiques %C Toulouse %U http://archive.numdam.org/articles/10.5802/afst.1162/ %R 10.5802/afst.1162 %G en %F AFST_2007_6_16_3_635_0
Pila, Jonathan. The density of rational points on a pfaff curve. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 16 (2007) no. 3, pp. 635-645. doi : 10.5802/afst.1162. http://archive.numdam.org/articles/10.5802/afst.1162/
[1] Bombieri (E) and Pila (J.).— The number of integral points on arcs and ovals, Duke Math. J. 59, p. 337-357 (1989). | MR | Zbl
[2] van den Dries (L.).— Tame topology and -minimal structures, LMS Lecture Note Series 248, CUP, Cambridge, (1998). | Zbl
[3] Gabrielov (A.) and Vorobjov (N.).— Complexity of computations with pfaffian and noetherian functions, in Normal Forms, Bifurcations and Finiteness problems in Differential Equations, Kluwer, (2004). | MR
[4] Gwozdziewicz (J.), Kurdyka (K.), Parusinski (A.).— On the number of solutions of an algebraic equation on the curve , and a consequence for o-minimal structures, Proc. Amer. Math. Soc. 127, p. 1057-1064 (1999). | MR | Zbl
[5] Khovanskii (A. G.).— Fewnomials, Translations of Mathematical Monographs 88, AMS, Providence, (1991). | MR | Zbl
[6] Pila (J.).— Integer points on the dilation of a subanalytic surface, Quart. J. Math. 55, p. 207-223 (2004). | MR | Zbl
[7] Pila (J.).— Rational points on a subanalytic surface, Ann. Inst. Fourier 55, p. 1501-1516 (2005). | Numdam | MR | Zbl
[8] Pila (J.).— Note on the rational points of a pfaff curve, Proc. Edin. Math. Soc., 49 (2006), 391-397. | MR | Zbl
[9] Pila (J.).— Mild parameterization and the rational points of a pfaff curve, Commentari Mathematici Universitatis Sancti Pauli, 55 (2006), 1-8. | MR | Zbl
[10] Pila (J.) and Wilkie (A. J.).— The rational points of a definable set, Duke Math. J., 133 (2006), 591-616. | MR | Zbl
[11] Pólya (G.).— On the zeros of the derivative of a function and its analytic character, Bull. Amer. Math. Soc. 49, 178-191 (1943). Also Collected Papers: Volume II, MIT Press, Cambridge Mass., p. 394-407 (1974). | MR | Zbl
[12] Waldschmidt (M.).— Diophantine approximation on linear algebraic groups, Grund. Math. Wissen. 326, Springer, Berlin, (2000). | MR | Zbl
[13] Wilkie (A. J.).— A theorem of the complement and some new o-minimal structures, Selecta Math. (N. S.) 5, p. 397-421 (1999). | MR | Zbl
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