p-Density, exponential sums and Artin-Schreier curves

Abstract

In this paper we define the $p$-density of a finite subset $D\subset\ma{N}^r$, and show that it gives a good lower bound for the $p$-adic valuation of exponential sums over finite fields of characteristic $p$. We also give an application: when $r=1$, the $p$-density is the first slope of the generic Newton polygon of the family of Artin-Schreier curves associated to polynomials with their exponents in $D$.

12 pages

Cited by in corpus (5)

• First vertices for generic Newton polygons, and $p$-cyclic coverings of the projective line
• On the $p$-integrality of $A$-hypergeometric series
• Congruences for L-functions of additive exponential sums
• Hasse invariants and mod $p$ solutions of $A$-hypergeometric systems
• Families of Artin-Schreier curves with Cartier-Manin matrix of constant rank