Ghorpade

Maximum number of zeroes of polynomials on weighted projective spaces over a finite field

arXiv:2507.22597v2 Announce Type: replace-cross Abstract: We compute the maximum number of rational points at which a homogeneous polynomial can vanish on a weighted projective space over a finite field, provided that the first weight is equal to one. This solves a conjecture by Aubry, Castryck, Ghorpade, Lachaud, O'Sullivan and Ram, which stated that a Serre-like bound holds with equality for weighted projective spaces when the first weight is one, and when considering polynomials whose...