Bounded Rational Points on Curves

We establish the uniform estimate <<<inf>d</inf>N2/d for the number of rational points of height at most N on an irreducible curve of degree d. We deduce this from a result for general hypersurfaces that is sensitive to the coefficients of the corresponding form. © 2014 The Author(...

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Autor principal: Walsh, M.N
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Lenguaje:Inglés
Publicado: Oxford University Press 2015
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245 1 0 |a Bounded Rational Points on Curves 
260 |b Oxford University Press  |c 2015 
270 1 0 |m Walsh, M.N.; Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos AiresArgentina 
506 |2 openaire  |e Política editorial 
504 |a Bombieri, E., Pila, J., The number of integral points on arcs and ovals (1989) Duke Mathematical Journal, 59 (2), pp. 337-357 
504 |a Bombieri, E., Vaaler, J., On Siegel's lemma (1983) Inventiones Mathematicae, 73 (1), pp. 11-32 
504 |a Broberg, N., A note on a paper by R. Heath-Brown: 'The density of rational points on curves and surfaces' (2004) Journal Für Die Reine und Angewandte Mathematik, 2004 (571), pp. 159-178 
504 |a Browning, T., Quantitative arithmetic of projective varieties (2009) Progress in Mathematics, 277. , Basel: Birkh äuser 
504 |a Browning, T., Heath-Brown, D.R., Counting rational points on hypersurfaces (2005) Journal Für Die Reine und Angewandte Mathematik, 2005 (584), pp. 83-115 
504 |a Browning, T., Heath-Brown, D.R., Salberger, P., Counting rational points on algebraic varieties (2006) Duke Mathematical Journal, 132 (3), pp. 545-578 
504 |a Ellenberg, J., Venkatesh, A., On uniform bounds for rational points on nonrational curves (2005) International Mathematics Research Notices, 2005 (5), pp. 2163-2181 
504 |a Fulton, W., Intersection theory (1984) Ergebnisse der Mathematik und Ihrer Grenzgebiete, (3), p. 2. , Berlin: Springer. Results in Mathematics and Related Areas (3) 
504 |a Heath-Brown, D.R., The density of rational points on curves and surfaces (2002) Annals of Mathematics, 155 (2), pp. 553-595. , Second Series 
504 |a Heath-Brown, D.R., Testa, D., Counting rational points on cubic curves (2010) Science China Mathematics, 53 (9), pp. 2259-2268 
504 |a Marmon, O., A generalization of the Bombieri-Pila determinant method (2010) Journal of Mathematical Sciences (New York), 171 (6), pp. 736-744 
504 |a Rault, P.X., On uniform bounds for rational points on rational curves of arbitrary degree (2013) Journal of Number Theory, 133 (9), pp. 3112-3118 
504 |a Salberger, P., On the density of rational and integral points on algebraic varieties (2007) Journal Für Die Reine und Angewandte Mathematik, 2007 (606), pp. 123-147 
504 |a Salberger, P., Counting Rational Points on Projective Varieties, , preprint 
504 |a Schmidt, W.M., Equations over finite fields. An elementary approach (1976) Lecture Notes in Mathematics, 536. , Berlin: Springer 
520 3 |a We establish the uniform estimate <<<inf>d</inf>N2/d for the number of rational points of height at most N on an irreducible curve of degree d. We deduce this from a result for general hypersurfaces that is sensitive to the coefficients of the corresponding form. © 2014 The Author(s) 2014. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.  |l eng 
593 |a Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires, 1428, Argentina 
773 0 |d Oxford University Press, 2015  |g v. 2015  |h pp. 5644-5658  |k n. 14  |p Int. Math. Res. Not.  |x 10737928  |t International Mathematics Research Notices 
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