On Manin's conjecture for a certain singular cubic surface |
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| Authors: | Ré gis de la Bretè che |
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| Affiliation: | UMR 7586, Case 7012, Université Paris 7 - Denis Diderot, 2, place Jussieu, F-75251 Paris cedex 05, France; School of Mathematics, University of Bristol, Bristol BS8 1TW, UK; Institut für Mathematik, Universität Zürich, Winterthurerstrasse 190, 8057 Zürich, Switzerland |
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| Abstract: | This paper contains a proof of the Manin conjecture for the singular cubic surface S⊂P3 that is defined by the equation  . In fact if U⊂S is the Zariski open subset obtained by deleting the unique line from S, and H is the usual exponential height on P3(Q), then the height zeta function ∑x∈U(Q)H(x)−s is analytically continued to the half-plane  . |
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