Linear relations among roots of a polynomial

2018/10/16 by Yoshiyuki Kitaoka, Kitaoka, Yoshiyuki
Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory #FOS: Mathematics #Meromorphic and Entire Functions #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1810.06791

openalex publication_date 2018/10/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let f(x) be a monic polynomial over ℚ with complex roots α₁,…,α_n. Linear relations among them and 1 over ℚ play an important role when we study the distribution of roots modulo a prime. We study linear relations group-theoretically. If ℚ(α₁) is an abelian extension, we can understand the structure completely.

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