Hybrid bounds for prime divisors

2024/11/13 by Gustav Kjærbye Bagger, Bagger, Gustav Kjærbye · 2 citations
Mathematics · #Rings, Modules, and Algebras #Advanced Topics in Algebra #Analytic Number Theory Research

paper · pdf · doi:10.48550/arxiv.2412.00010

Abstract

Let x and n be positive integers. We prove a non-trivial lower bound for x, dependant only on ω_n, the number of distinct prime factors of xⁿ-1. By considering the divisibility of φ| xⁿ-1 for φ| n, we obtain a further refinement. This bound has applications for existence problems relating to primitive elements in finite fields.

Cited by

• Normal and primitive normal elements with prescribed traces in intermediate extensions of finite fields
• The modified prime sieve for primitive elements in finite fields

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