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On a certain non-split cubic surface

Abstract : In this note, we establish an asymptotic formula with a power-saving error term for the number of rational points of bounded height on the singular cubic surface of P 3 Q x 0 (x 2 1 + x 2 2) = x 3 3 in agreement with the Manin-Peyre conjectures.
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Régis de la Bretèche, Kévin Destagnol, Jianya Liu, Jie Wu, Yongqiang Zhao. On a certain non-split cubic surface. Science China Mathematics, Science China Press, 2019, 62 (12), pp.2435-2446. ⟨10.1007/s11425-018-9543-8⟩. ⟨hal-02468799⟩

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