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On the Number of Rational Points of Hypersurfaces over Finite Fields

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Abstract.

We prove the existence of hypersurfaces defined over finite fields having a prescribed number of \({\mathbb{F}}_{q}\)-rational points and a prescribed number of non-singular points. Moreover, some results on \({\mathbb{F}}_{q}\)-rational intersections between plane curves, lines and conics, are given.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università di Trento, I-38050, Povo, TN, Italy

    Edoardo Ballico

  2. Dipartimento di Matematica e Informatica, Università di Basilicata, I-85100, Potenza, Italy

    Antonio Cossidente

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  1. Edoardo Ballico
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  2. Antonio Cossidente
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Correspondence to Edoardo Ballico.

Additional information

The first author was partially supported by MIUR and GNSAGA of INdAM (Italy).

Received: June 1, 2006. Revised: August 1, 2007.

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Ballico, E., Cossidente, A. On the Number of Rational Points of Hypersurfaces over Finite Fields. Result. Math. 51, 1–4 (2007). https://doi.org/10.1007/s00025-007-0253-5

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  • DOI: https://doi.org/10.1007/s00025-007-0253-5

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