REVIEW
On irreducible polynomials over finite fields
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
On irreducible polynomials over finite fields
classification
math.NT
math.CO
keywords
strictlyfiniteincreasingirreduciblepolynomialssequencedecreasingdenote
read the original 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.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.