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August 3, 2026International Journal of Number TheoryOpen Access

Infinite products with algebraic numbers

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Authors

SKSimon KristensenMLMathias L. Laursen

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Overview

We report criteria for lower bounds on the degree of algebraic numbers in infinite products, implying new insights into algebraic structures.

Key Points

  • To establish general criteria for determining lower bounds on the degree of algebraic numbers expressed as infinite products.
  • Derived criteria based on growth conditions of involved algebraic integers and natural numbers.
  • Analyzed expressions for arbitrary algebraic integers and natural number components.
  • Identified the smallest extension containing all relevant algebraic quantities.
  • Provided lower bounds on the degree of given algebraic numbers.
  • Showed dependence of criteria on specific growth conditions.
  • Highlighted how criteria can be applied to various algebraic expressions.

Cite This Study

Kristensen et al. (2026) studied this question.

synapsesocial.com/papers/6a703fe175942ff7265e487bhttps://doi.org/10.1142/s1793042126501344
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