Subgroups Generated by Rational Functions in Finite Fields

2013/09/27 by Domingo Gómez‐Pérez, Gomez-Perez, Domingo, Igor E. Shparlinski +1
Computer Science · Mathematics · #Analytic Number Theory Research #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1309.7378

openalex publication_date 2013/09/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a large prime p, a rational function ψ∈ F_p(X) over the finite field F_p of p elements, and integers u and H≥ 1, we obtain a lower bound on the number consecutive values ψ(x), x = u+1, …, u+H that belong to a given multiplicative subgroup of F_p^*.

Citations

• Points on curves in small boxes en applications

Related

• Polynomial Values in Small Subgroups of Finite Fields
• Sparsity of curves and additive and multiplicative expansion of rational maps over finite fields
• Values of rational functions in small subgroups of finite fields and the\n identity testing problem from powers
• Multiplicative dependence modulo subsets
• Unlikely intersections over finite fields: polynomial orbits in small subgroups