A Combinatorial Approach to the Number of Solutions of Systems of Homogeneous Polynomial Equations over Finite Fields

2018/07/04 by Beelen, Peter, Datta, Mrinmoy, Ghorpade, Sudhir R. · 1 citation
#11G25 #14G05 #51E20 #94B27 #Algebraic Geometry (math.AG) #FOS: Mathematics #Primary 14G15 #Secondary 11T71

paper · doi:10.48550/arxiv.1807.01683

Abstract

We give a complete conjectural formula for the number e_r(d,m) of maximum possible \mathbbFq-rational points on a projective algebraic variety defined by r linearly independent homogeneous polynomial equations of degree d in m+1 variables with coefficients in the finite field \mathbbFq with q elements, when d

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