3 papers
math.AG2025
Maximum number of rational points on hypersurfaces in weighted projective spaces over finite fields
Yves Aubry, Marc Perret
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.…
math.AG2025
Corrigendum to the paper "Maximum number of rational points on hypersurfaces in weighted projective spaces over finite fields", Journal of Algebra and Its Applications, Vol. 24, No. 13n14, 2541015(2025)
Yves Aubry, Marc Perret
The statement of item (ii) of Proposition 3.2 of the article referenced in the title is not correct. We provide a corrected version and show that, under the assumption that $\gcd(a…
math.NT2025
Refinements on higher order Weil-Oesterlé bounds via a Serre type argument
Emmanuel Hallouin, Philippe Moustrou, Marc Perret
Weil's theorem gives the most standard bound on the number of points of a curve over a finite field. This bound was improved by Ihara and Oesterlé for larger genus. Recently, Hall…