Generalization of a Theorem of Carlitz

Details Generalization of a Theorem of Carlitz Generalization of a Theorem of Carlitz

2010-03-30

arxiv.org/abs/1003.5856v1

Mathematics

Number Theory

10 pages

Scientific paper

We generalize Carlitz' result on the number of self reciprocal monic
irreducible polynomials over finite fields by showing that similar explicit
formula hold for the number of irreducible polynomials obtained by a fixed
quadratic transformation. Our main tools are a combinatorial argument and
Hurwitz genus formula.

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