Irreducible polynomials over finite fields with prescribed trace/prescribed constant term

We obtain an equivalent version of Carlitz's formula for the number of monic irreducible polynomials of degree n and trace γ ≠ 0 over a finite field via an integer recurrence. Similar expressions for the γ = 0 case are also given. We also obtain formulas for the number of monic irreducible poly...

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Bibliographic Details
Published in:Finite fields and their applications 2006-04, Vol.12 (2), p.211-221
Main Author: Yucas, Joseph L.
Format: Article
Language:English
Subjects:
Finite field
Polynomials
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Summary:We obtain an equivalent version of Carlitz's formula for the number of monic irreducible polynomials of degree n and trace γ ≠ 0 over a finite field via an integer recurrence. Similar expressions for the γ = 0 case are also given. We also obtain formulas for the number of monic irreducible polynomials of degree n and prescribed constant term.
ISSN:1071-5797
1090-2465
DOI:10.1016/j.ffa.2005.04.006