  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 $D$.
