2015/02/03 by Régis Blache, Blache, Régis
Computer Science · Mathematics · #11L #14H #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Coding theory and cryptography #FOS: Mathematics #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.1502.00969
openalex publication_date 2015/02/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let p denote an odd prime. In this paper, we are concerned with the p-divisibility of additive exponential sums associated to one variable polynomials over a finite field of characteristic p, and with (the very close question of) determining the Newton polygons of some families of Artin-Schreier curves, i.e. p-cyclic coverings of the projective line in characteristic p. We first give a lower bound on the p-divisibility of exponential sums associated to polynomials of fixed degree. Then we show that an Artin-Schreier curve defined over a finite field of characteristic p cannot be supersingular when its genus g has the form (p-1)(i(pn-1)-1)/2 for some 1≤ i≤ p-1 and n≥ 1 such that n(p-1)>2. We also determine the first vertex of the generic Newton polygon of the family of p-rank 0 Artin-Schreier curves of fixed genus, and the associated Hasse polynomial.