On maximal and minimal hypersurfaces of Fermat type

2021/10/14 by José Alves Oliveira, Oliveira, José Alves · 1 citation
Mathematics · Arts and Humanities · #Algebraic Geometry and Number Theory #Historical Studies and Socio-cultural Analysis

paper · pdf · doi:10.48550/arxiv.2110.07452

Abstract

Let \mathbbF_q be a finite field with q=pⁿ elements. In this paper, we study the number of \mathbbF_q-rational points on the affine hypersurface \mathcal X given by a₁ x₁^d₁+…+a_s x_s^d_s=b, where b∈\mathbbF_q^*. A classic well-konwn result from Weil yields a bound for such number of points. This paper presents necessary and sufficient conditions for the maximality and minimality of \mathcal X with respect to Weil's bound.

Cited by

• On \mathbbF_q-primitive points on hypersurfaces

Related

• On \mathbbF_q-primitive points on hypersurfaces
• Maximum number of rational points on hypersurfaces in weighted projective spaces over finite fields
• On the number of rational points of Artin-Schreier curves and hypersurfaces
• Rational linear subspaces of hypersurfaces over finite fields
• Counting rational points on hypersurfaces