Linear relations among roots of a polynomial

Yoshiyuki Kitaoka

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arXiv · 1810.06791

Linear relations among roots of a polynomial

Yoshiyuki Kitaoka

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Abstract

Let $f(x)$ be a monic polynomial over $\mathbb{Q}$ with complex roots $\alpha_1,\dots,\alpha_n$. Linear relations among them and $1$ over $\mathbb{Q}$ play an important role when we study the distribution of roots modulo a prime. We study linear relations group-theoretically. If $\mathbb{Q}(\alpha_1)$ is an abelian extension, we can understand the structure completely.

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Yoshiyuki Kitaoka. 2018-10-16. Linear relations among roots of a polynomial. https://arxiv.org/abs/1810.06791

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