Multiplicative relations with conjugate algebraic numbers

• Date: 2007
• Main Authors: Dubickas, A., Дубікас, А.
• Format: Article
• Language: English
• Published: Institute of Mathematics, NAS of Ukraine 2007
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/3354
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We study what algebraic numbers can be represented by a product of algebraic numbers conjugate over a fixed number field K in fixed integer powers. The problem is nontrivial if the sum of these integer powers is equal to zero. The norm of such a number over K must be a root of unity. We show that th...