On the Complexity of &lt;i&gt;p&lt;/i&gt;-Adic Continued Fractions of Rational Number

Belhadef, Rafik; Esbelin, Henri-Alex

doi:10.12691/tjant-10-1-2

TJANT

2022

DOI: 10.12691/tjant-10-1-2

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On the Complexity of <i>p</i>-Adic Continued Fractions of Rational Number

Rafik Belhadef¹,

Henri-Alex Esbelin²

Abstract: In this paper, we study the complexity of p-adic continued fractions of a rational number, which is the p-adic analogue of the theorem of Lamé. We calculate the length of Browkin expansion, and the length of Schneider expansion. Also, some numerical examples have been given.

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2024

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Continued fractions in the field of 𝑝-adic numbers

Romeo

2024

Bull. Amer. Math. Soc.

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Continued fractions have a long history in number theory, especially in the area of Diophantine approximation. The aim of this expository paper is to survey the main results on the theory of p p -adic continued fractions, i.e., continued fractions defined over the field of p p -adic numbers Q p \mathbb {Q}_p , which in the last years has recorded a considerable increase of interest and research activity. We start from the very first definitions up to the most recent developments and open problems.

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Continued fractions in the field of 𝑝-adic numbers

Romeo

2024

Bull. Amer. Math. Soc.

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scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

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On the Complexity of <i>p</i>-Adic Continued Fractions of Rational Number

Abstract: In this paper, we study the complexity of p-adic continued fractions of a rational number, which is the p-adic analogue of the theorem of Lamé. We calculate the length of Browkin expansion, and the length of Schneider expansion. Also, some numerical examples have been given.

Cited by 1 publication

References 8 publications

Continued fractions in the field of 𝑝-adic numbers

Continued fractions in the field of 𝑝-adic numbers

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