2024/06/05 by Kajari Chatterjee, Chatterjee, K., S. K. Tiwari +1
Biochemistry, Genetics and Molecular Biology · Computer Science · Decision Sciences · #11T23 #12E20 #Connective tissue disorders research #FOS: Mathematics #Fuzzy and Soft Set Theory #Number Theory (math.NT) #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2406.03571
openalex publication_date 2024/06/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For any positive integers q, n, m with q being a prime power and n ≥ 5, we establish a condition sufficient to ensure the existence of a primitive normal pair (ε,f(ε)) in \mathbbFqn over \mathbbFq such that PNqn/q(ε)=a, where a∈\mathbbFq is prescribed. Here f=f1/f2∈\mathbbFqn(x) is a rational function subject to some minor restrictions such that deg(f1)+deg(f2)=m and PNqn/q(ε) =∑i=0n-1(\undersetj≠ i\underset0≤ j≤ n-1∏εqj). Finally, we conclude that for m=3, n≥ 6, and q=7k where k∈ℕ, such a pair will exist certainly for all (q,n) except possibly 10 choices at most.