Pizzato, Marco (2013) *Some Problems Concerning Polynomials over Finite Fields, or Algebraic Divertissements.* PhD thesis, University of Trento.

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## Abstract

In this thesis we consider some problems concerning polynomials over finite fields. The first topic is the action of some groups on irreducible polynomials. We describe orbits and stabilizers. Next, we consider transformations of irreducible polynomials by quadratic and cubic maps and study the irreducibility of the polynomials obtained. Finally, starting from PN functions and monomials, we generalize this concept, introducing k-PN monomials and classifying them for small values of k and for fields of order p, p^2 and p^4.

Item Type: | Doctoral Thesis (PhD) |
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Doctoral School: | Mathematics |

PhD Cycle: | XXV |

Subjects: | Area 01 - Scienze matematiche e informatiche > MAT/02 ALGEBRA |

Repository Staff approval on: | 19 Dec 2013 16:10 |

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