On irreducible polynomials over finite fields
Abstract
For n=1,2,3,... let Nn(q) denote the number of monic irreducible polynomials over the finite field Fq. We mainly show that the sequence Nn(q)1/n (n>e3+7/(q-1)2) is strictly increasing and the sequence Nn+1(q)1/(n+1)/Nn(q)1/n (n>=5.835*1014) is strictly decreasing. We also prove that if q>8 then Nn+1(q)/Nn(q) (n=1,2,3,...) is strictly increasing.
0
Turn this paper into a lesson
ArcXiv compiles a structured reading guide from this paper's metadata: plain-English importance, contributions, prerequisite concepts, which sections to read first, flashcards, and a quiz. Grounded in the abstract, never invented.