Maximum number of rational points on hypersurfaces in weighted projective spaces over finite fields
An upper bound for the maximum number of rational points on a 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 Aubry, Castryck, Ghorpade, Lachaud, O’Sullivan and Ram in 2017. A conjecture has been proposed there under the assumption that the first weight is equal to one 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.
Authors
- Yves Aubry (ORCID: https://orcid.org/0000-0003-2095-252X)
- Marc Perret
Institutions
- Centre National de la Recherche Scientifique (FR)
- Université Toulouse III - Paul Sabatier (FR)
- Université de Toulon (FR)
- Institut National des Sciences Appliquées de Toulouse (FR)
- Toulouse Mathematics Institute (FR)
- Château Gombert (FR)
- Institut de Mathématiques de Marseille (FR)
- Université Toulouse - Jean Jaurès (FR)
- Institut Polytechnique de Bordeaux (FR)
- Institut de Mathématiques de Toulouse (FR)
Publication Details
- Journal
- Journal of Algebra and Its Applications
- Published
- 2025-02-13
- DOI
- https://doi.org/10.1142/s0219498825410154
- Citations
- 1
- Primary Topic
- Algebraic Geometry and Number Theory
- Type
- article
- Field-Weighted Citation Impact
- 4.09
Funders
- Agence Nationale de la Recherche