On irreducible polynomials over finite fields

Zhi-Wei Sun

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arXiv · 1210.1562

On irreducible polynomials over finite fields

Zhi-Wei Sun

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Abstract

For n=1,2,3,... let N_n(q) denote the number of monic irreducible polynomials over the finite field F_q. We mainly show that the sequence N_n(q)^{1/n} (n>e^{3+7/(q-1)^2}) is strictly increasing and the sequence N_{n+1}(q)^{1/(n+1)}/N_n(q)^{1/n} (n>=5.835*10^{14}) is strictly decreasing. We also prove that if q>8 then N_{n+1}(q)/N_n(q) (n=1,2,3,...) is strictly increasing.

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BibTeX RIS

Zhi-Wei Sun. 2012-10-15. On irreducible polynomials over finite fields. https://arxiv.org/abs/1210.1562

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