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Israel Journal of Mathematics

, Volume 94, Issue 1, pp 59–91 | Cite as

Reducibility behavior of polynomials with varying coefficients

  • Peter Müller
Article

Abstract

LetK be a number field, and lethK[Y] be a polynomial of degreen. Fix an integer 0≤i≤n and compare the set ν of those integersa ofK such thath(Y)−aY ihas a root inK with the set\(\mathcal{R}\) of those integersa, such thath(Y)−aY iis reducible overK. Ifi is coprime ton, then we classify the rare cases where ν is not cofinite in\(\mathcal{R}\). The main tools are a theorem of Siegel about integral points on algebraic curves and the theory of finite groups.

Keywords

Normal Subgroup Finite Group Permutation Group Number Field Algebraic Closure 
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

© The Magnes Press 1996

Authors and Affiliations

  • Peter Müller
    • 1
  1. 1.Mathematisches InstitutUniversität Erlangen-NürnbergErlangenGermany

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