Journal of the Australian Mathematical Society

Research Article

On the pseudorandomness of the signs of Kloosterman sums

Étienne Fouvrya1, Philippe Michela2, Joël Rivata3 and András Sárközya4

a1 Mathématique, Bâtiment 425, Campus d'Orsay, Université Paris-Sud, 91405 Orsay Cedex, France e-mail: etienne.fouvry@math.u-psud.fr

a2 Mathématiques, Université Montpellier II, CC 052, 34095 Montpellier Cedex, France e-mail: philippe.michel@math.univ-montp2.fr

a3 Institut de Mathématiques de Luminy, CNRS-UMR 6206, Université de la Méditerranée, 163 avenue de Luminy, Case 907, 13288 Marseille Cedex 9, France e-mail: rivat@iml.univ-mrs.fr

a4 Eötvös Loránd University, Department of Algebra, and Number Theory, H-1117 Budapest, Pázmány Péter sétány 1/c, Hungary e-mail: sarkozy@cs.elte.hu

Abstract

In this paper we study the pseudorandom properties of the signs of Kloosterman sums.

(Received February 17 2003)

(Revised September 29 2003)

2000 Mathematics subject classification

  • primary 11K36;
  • 11L05;
  • secondary 11K45;
  • 11K38

Keywords and phrases

  • Pseudo-random;
  • binary sequence;
  • correlation;
  • Kloosterman sums;
  • monodromy