Cubic surfaces over finite fields
Published online by Cambridge University Press: 07 July 2010
Extract
Let V be a nonsingular cubic surface defined over the finite field Fq. It is well known that the number of points on V satisfies #V(Fq) = q2 + nq + 1 where −2 ≤ n ≤ 7 and that n = 6 is impossible; see for example [1], Table 1. Serre has asked if these bounds are best possible for each q. In this paper I shall show that this is so, with three exceptions:
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- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 149 , Issue 3 , November 2010 , pp. 385 - 388
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- Copyright © Cambridge Philosophical Society 2010
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