Maximum number of rational points on hypersurfaces in weighted projective spaces over finite fields
Year: 2025
Type: article
Abstract: 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, Marc Perret
Institutions: Centre National de la Recherche Scientifique, Université de Toulon, Aix-Marseille Université, Institut de Mathématiques de Marseille, Institut de Mathématiques de Toulon, Université Toulouse III - Paul Sabatier, Institut National des Sciences Appliquées de Toulouse, Université Toulouse - Jean Jaurès, Institut de Mathématiques de Toulouse
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Agence Nationale de la Recherche
OpenAlex ID: W4391740261