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1 I2M - Institut de Mathématiques de Marseille 2 IMATH - Institut de Mathématiques de Toulon - EA 2134 3 KU Leuven - Katholieke Universiteit Leuven 4 LPP - Laboratoire Paul Painlevé 5 IIT Bombay - Indian Institute of Technology Bombay 6 San Diego State University 7 HRI - Harish-Chandra Research Institute

Abstract : We consider the question of determining the maximum number of Fq-rational points that can lie on a hypersurface of a given degree in a weighted projective space over the finite field Fq, or in other words, the maximum number of zeros that a weighted homogeneous polynomial of a given degree can have in the corresponding weighted projective space over Fq.
In the case of classical projective spaces, this question has been answered by J.-P.
Serre.
In the case of weighted projective spaces, we give some conjectures and partial results.
Applications to coding theory are included and an appendix providing a brief compendium of results about weighted projective spaces is also included.






Autor: Yves Aubry - Wouter Castryck - Sudhir Ghorpade - Gilles Lachaud - Michael O -Sullivan - Samrith Ram -

Fuente: https://hal.archives-ouvertes.fr/



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