Article Dans Une Revue Journal of Algebra and Its Applications Année : 2025

MAXIMUM NUMBER OF RATIONAL POINTS ON HYPERSURFACES IN WEIGHTED PROJECTIVE SPACES OVER FINITE FIELDS

Résumé

An upper bound for the maximum number of rational points on an hypersurface in a projective space over a finite field has been conjectured by Tsfasman and proved by Serre in 1989. The analogue question for hypersurfaces on weighted projective spaces has been considered by Castryck, Ghorpade, Lachaud, O'Sullivan, Ram and the first author in 2017. A conjecture has been proposed there and proved in the particular case of the dimension 2. We prove here the conjecture in any dimension provided the second weight is also equal to one.

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Dates et versions

hal-04449392 , version 1 (09-02-2024)
hal-04449392 , version 2 (29-11-2025)

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Yves Aubry, Marc Perret. MAXIMUM NUMBER OF RATIONAL POINTS ON HYPERSURFACES IN WEIGHTED PROJECTIVE SPACES OVER FINITE FIELDS. Journal of Algebra and Its Applications, 2025. ⟨hal-04449392v2⟩
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