Abstract
An upper bound of the expected order of magnitude is established for the number of \({\mathbb Q}\)-rational points of bounded height on Châtelet surfaces defined over \({\mathbb Q}\).
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de la Bretèche R., Browning T.D.: Sums of arithmetic functions over values of binary forms. Acta Arith. 125, 291–304 (2007)
Browning T.D., Heath-Brown D.R.: Counting rational points on hypersurfaces. J. Reine Angew. Math. 584, 83–115 (2005)
Colliot-Thélène J.-L., Sansuc J.-J., Swinnerton-Dyer P.: Intersections of two quadrics and Châtelet surfaces. I. J Reine Angew. Math. 373, 37–107 (1987)
Colliot-Thélène J.-L., Sansuc J.-J., Swinnerton-Dyer P.: Intersections of two quadrics and Châtelet surfaces. II. J Reine Angew. Math. 374, 72–168 (1987)
Dedekind R.: Gesammelte Mathematische Werke, Band, vol. 1. Friedr. Vieweg & Sohn, Braunschweig (1930)
Franke J., Manin Y.I., Tschinkel Y.: Rational points of bounded height on Fano varieties. Invent. Math. 95, 421–435 (1989)
Heilbronn, H.: Zeta-functions and L-functions. Algebraic Number Theory (Proc. Instructional Conf., Brighton, 1965), pp. 204–230. Academic Press, London (1967)
Iskovskikh V.A.: Minimal models of rational surfaces over arbitrary fields. Math. USSR Izv. 14, 17–39 (1980)
Iwaniec, H., Munshi, R.: Cubic polynomials and quadratic forms. Proc. Lond. Math. Soc. (2009, to appear)
Leung, F.-S.: Manin’s conjecture on a non-singular quartic del Pezzo surface. D.Phil thesis, Oxford (2008)
Narkiewicz, W.: Elementary and analytic theory of algebraic numbers, 3rd edn. Springer Monographs in Math., Springer, Heidelberg (2004)
Neukirch J.: Algebraic number theory. Grund. Math. Wissenschaften. vol. 322. Springer, Heidelberg (1999)
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Browning, T.D. Linear growth for Châtelet surfaces. Math. Ann. 346, 41–50 (2010). https://doi.org/10.1007/s00208-009-0383-z
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DOI: https://doi.org/10.1007/s00208-009-0383-z