Divisibility of L-Polynomials for a Family of Artin-Schreier Curves

Dr. Emrah Sercan Yilmaz

18 March 2022 17:00

Abstract

In this talk we consider the curves C_k^(p,a) : y^p − y = x^{p^k+1} + ax defined over F_p and k give a positive answer to a conjecture about a divisibility condition on L-polynomials of the curves C_k^(p,a). Our proof involves finding an exact formula for the number of F_{p^n} -rational points on C_k^(p,a) for all n, and uses a result we proved elsewhere about the k number of rational points on supersingular curves.