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July 26, 2026The Ramanujan JournalOpen Access

On some periodic continued fractions along the Z₂ extension over Q

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Authors

YKYoshinori KanamuraHYHyuga Yoshizaki

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Overview

Constructs explicit periodic continued fractions in the Z2 extension of number fields, suggesting new avenues for exploration.

Key Points

  • The aim is to construct periodic continued fractions for specific values in the Z2 extension of rational numbers.
  • Constructed bijections between subsets of relative units in the Z2 extension and sets of periodic continued fractions.
  • Focused on (1, 2) and (0, 3)-type continued fractions for Xn.
  • Provided explicit bounds for the logarithms of relative units corresponding to these types.
  • Successfully constructed (1, 2) and (0, 3)-type periodic continued fractions for Xn for all n≥1.
  • Confirmed the existence of these continued fractions in specified types.
  • Determined bounds for logarithmic values of relative units that elucidate their distribution behavior.

Cite This Study

Kanamura et al. (2026) studied this question.

synapsesocial.com/papers/6a65a2e2d3aea3239cd76296https://doi.org/10.1007/s11139-026-01423-4
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