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manuscripta mathematica

, Volume 62, Issue 2, pp 187–203 | Cite as

Irreducible factors of psi-polynomials over finite fields

  • Ulrich Schoenwaelder
Article
  • 23 Downloads

Abstract

An invertible 2 by 2 matrix\(C = (\begin{array}{*{20}c} \alpha & \beta \\ \gamma & \delta \\ \end{array} \) over the finite fieldF withq elements defines a linear fractional transformation on the projective line over the algebraic closureK ofF. The irreducible polynomials overF whose zero sets are invariant under this action ofC are the irreducible factors of Ore's psi-polynomials ψ c,k fork=0,1,2... We study the factorization of these polynomials into components. A component is defined as the product of all monic, irreducible factors of a fixed degree. It is shown in a uniform proof which factor degrees occur in components of ψ c,k and that in an inductive procedure onk over all generators¯C′ of 〈(¯C〉 inPGL(2,F) just one “new” component occurs in ψc,k which therefore can be computed by a division of ψc′,k by its previously determined components of smaller factor degree.

Keywords

Number Theory Algebraic Geometry Topological Group Finite Field Projective Line 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • Ulrich Schoenwaelder
    • 1
  1. 1.Lehrstuhl D Für MathematikRwth AachenAachenFRG

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