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hal-00551478, version 1

p-Density, exponential sums and Artin-Schreier curves

Régis Blache 1

(2008-12-17)

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 $D$.

  • 1:  Laboratoire de Mathématiques Informatique et Applications (LAMIA)
  • Université des Antilles et de la Guyane
  • Domain : Mathematics/Number Theory
    Mathematics/Algebraic Geometry
  • Keywords : Character sums – $L$-functions – Newton polygons – Chevalley-Warning theorem
 
  • hal-00551478, version 1
  • http://hal.archives-ouvertes.fr/hal-00551478
  • oai:hal.archives-ouvertes.fr:hal-00551478
  • From: Régis Blache <>
  • Submitted on: Monday, 3 January 2011 18:33:27
  • Updated on: Monday, 3 January 2011 18:33:27