p-Density, exponential sums and Artin-Schreier curves

Details p-Density, exponential sums and Artin-Schreier curves p-Density, exponential sums and Artin-Schreier curves

2008-12-17

arxiv.org/abs/0812.3382v1

Mathematics

Number Theory

12 pages

Scientific paper

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 $D$.

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