Continued $$\beta $$ β -fractions with formal power series over finite fields

Hbaib, M.; Kammoun, Rania

doi:10.1007/s11139-015-9725-5

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2022

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“…Feng et al [19] proved that the metric properties of continued β-fraction expansion. For more results on the continued β-fraction with Laurent series in finite fields, we refer the reader to [20,21].…”

Section: Introductionmentioning

confidence: 99%

On the Eventually Periodic Continued β-Fractions and Their Lévy Constants

Xiao

Wang

2022

Mathematics

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In this paper, we consider continued β-fractions with golden ratio base β. We show that if the continued β-fraction expansion of a non-negative real number is eventually periodic, then it is the root of a quadratic irreducible polynomial with the coefficients in Z[β] and we conjecture the converse is false, which is different from Lagrange’s theorem for the regular continued fractions. We prove that the set of Lévy constants of the points with eventually periodic continued β-fraction expansion is dense in [c, +∞), where c=12logβ+2−5β+12.

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Section: Introductionmentioning

confidence: 99%