Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On irreducible polynomials over finite fields   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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The categories of this paper are: q-bio
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The categories of this paper are: eess
7
The categories of this paper are: hep-th
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The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: dg-ga
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-ph
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The categories of this paper are: patt-sol