On irreducible polynomials over finite fields

2012/10/04 by Zhi‐Wei Sun, Sun, Zhi-Wei
Computer Science · #Coding theory and cryptography #Cellular Automata and Applications #Cryptography and Residue Arithmetic

paper · pdf · doi:10.48550/arxiv.1210.1562

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*10¹⁴) 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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