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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Oxford University Press
2015
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| LEADER | 04311caa a22004577a 4500 | ||
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| 001 | PAPER-13604 | ||
| 003 | AR-BaUEN | ||
| 005 | 20230518204359.0 | ||
| 008 | 190411s2015 xx ||||fo|||| 00| 0 eng|d | ||
| 024 | 7 | |2 scopus |a 2-s2.0-84939612463 | |
| 040 | |a Scopus |b spa |c AR-BaUEN |d AR-BaUEN | ||
| 100 | 1 | |a Walsh, M.N. | |
| 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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| 856 | 4 | 0 | |u https://doi.org/10.1093/imrn/rnu103 |y DOI |
| 856 | 4 | 0 | |u https://hdl.handle.net/20.500.12110/paper_10737928_v2015_n14_p5644_Walsh |y Handle |
| 856 | 4 | 0 | |u https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10737928_v2015_n14_p5644_Walsh |y Registro en la Biblioteca Digital |
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| 999 | |c 74557 | ||