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We report criteria for lower bounds on the degree of algebraic numbers in infinite products, implying new insights into algebraic structures.
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.
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Kristensen et al. (2026) studied this question.
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