The density of rational points on a pfaff curve

Jonathan Pila[1]

  • [1] School of Mathematics, University of Bristol, Bristol, BS8 1TW (UK)

Annales de la faculté des sciences de Toulouse Mathématiques (2007)

  • Volume: 16, Issue: 3, page 635-645
  • ISSN: 0240-2963

Abstract

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This paper is concerned with the density of rational points on the graph of a non-algebraic pfaffian function.

How to cite

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Pila, Jonathan. "The density of rational points on a pfaff curve." Annales de la faculté des sciences de Toulouse Mathématiques 16.3 (2007): 635-645. <http://eudml.org/doc/10065>.

@article{Pila2007,
abstract = {This paper is concerned with the density of rational points on the graph of a non-algebraic pfaffian function.},
affiliation = {School of Mathematics, University of Bristol, Bristol, BS8 1TW (UK)},
author = {Pila, Jonathan},
journal = {Annales de la faculté des sciences de Toulouse Mathématiques},
language = {eng},
number = {3},
pages = {635-645},
publisher = {Université Paul Sabatier, Toulouse},
title = {The density of rational points on a pfaff curve},
url = {http://eudml.org/doc/10065},
volume = {16},
year = {2007},
}

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
PB - Université Paul Sabatier, Toulouse
VL - 16
IS - 3
SP - 635
EP - 645
AB - This paper is concerned with the density of rational points on the graph of a non-algebraic pfaffian function.
LA - eng
UR - http://eudml.org/doc/10065
ER -

References

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  4. Gwozdziewicz (J.), Kurdyka (K.), Parusinski (A.).— On the number of solutions of an algebraic equation on the curve y = e x + sin x , x &gt; 0 , and a consequence for o-minimal structures, Proc. Amer. Math. Soc.127, p. 1057-1064 (1999). Zbl0916.03026MR1476134
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  8. Pila (J.).— Note on the rational points of a pfaff curve, Proc. Edin. Math. Soc., 49 (2006), 391-397. Zbl1097.11037MR2243794
  9. Pila (J.).— Mild parameterization and the rational points of a pfaff curve, Commentari Mathematici Universitatis Sancti Pauli, 55 (2006), 1-8. Zbl1129.11029MR2251995
  10. Pila (J.) and Wilkie (A. J.).— The rational points of a definable set, Duke Math. J., 133 (2006), 591-616. Zbl1217.11066MR2228464
  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). Zbl0061.11510MR7781
  12. Waldschmidt (M.).— Diophantine approximation on linear algebraic groups, Grund. Math. Wissen. 326, Springer, Berlin, (2000). Zbl0944.11024MR1756786
  13. Wilkie (A. J.).— A theorem of the complement and some new o-minimal structures, Selecta Math. (N. S.)5, p. 397-421 (1999). Zbl0948.03037MR1740677

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