Infinite products with algebraic numbers
Abstract
We obtain general criteria for giving a lower bound on the degree of numbers of the form [Formula: see text] or of the form [Formula: see text], where the [Formula: see text] and [Formula: see text] are assumed to be algebraic integers, and the [Formula: see text] and [Formula: see text] are natural numbers. In each case, we give a lower bound of the degree over the smallest extension of [Formula: see text] containing all algebraic numbers in the expression. The criteria obtained depend on growth conditions on the involved quantities.
Fields of Study & Subjects
Computability
Logic
AI Algorithms
Publication details
- Journal / source
- International Journal of Number Theory
- Publisher
- World Scientific Pub Co Pte Ltd
- Pages
- 1–27
- Publication date
- 31 July 2026
- Language
- EN