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NOTE ON THE RATIONAL POINTS OF A PFAFF CURVE

Published online by Cambridge University Press:  30 May 2006

Jonathan Pila
Jonathan Pila
Affiliation:
Department of Mathematics and Statistics, McGill University, Burnside Hall, 805 Sherbrooke Street West, Montreal, Quebec H3A 2K6, Canada Mathematical Institute, University of Oxford, 24–29 St Giles’, Oxford OX1 3LB, UK
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Abstract

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Let $X\subset\mathbb{R}^2$ be the graph of a Pfaffian function $f$ in the sense of Khovanskii. Suppose that $X$ is non-algebraic. This note gives an estimate for the number of rational points on $X$ of height less than or equal to $H$; the estimate is uniform in the order and degree of $f$.

Keywords

Primary 11J99Secondary 11D99rational pointPfaff curveplane algebraic curve
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 49 , Issue 2 , June 2006 , pp. 391 - 397
Copyright
Copyright © Edinburgh Mathematical Society 2006