p-Density, exponential sums and Artin-Schreier curves

Régis Blache (1)

1 LAMIA - Laboratoire de Mathématiques Informatique et Applications

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 $D$.

Mots clés: Character sums; $L$-functions; Newton polygons; Chevalley-Warning theorem

Domaines: Théorie des nombres [math.NT]; Géométrie algébrique [math.AG]

Régis Blache. p-Density, exponential sums and Artin-Schreier curves. 2008. ⟨hal-00551478⟩