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Distribution of Irreducible Polynomials over F2

  • Kenneth H. Hicks
  • Gary L. Mullen
  • Ikuro Sato

Abstract

Using a polynomial analogue of the wheel sieve, we discuss the distribution of irreducible polynomials over F 2. In particular, we provide considerable numerical evidence that in analogue to integer arithmetic progressions, irreducible polynomials over F 2 are binomially distributed in the progressions of the wheel sieve. We also present, numerical evidence that the irreducibles of fixed degree are binomially distributed by weight. Also briefly discussed is the distribution of self-reciprocal irreducible polynomials. A number of conjectures are raised.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Kenneth H. Hicks
    • 1
  • Gary L. Mullen
    • 2
  • Ikuro Sato
    • 1
  1. 1.Department of PhysicsOhio UniversityAthensUSA
  2. 2.Department of MathematicsThe Pennsylvania State UniversityUniversity ParkUSA

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