Palindromic p-adic continued fractions-Reference-Cited by-同舟云学术

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Palindromic p-adic continued fractions

Published:2022 Issue:4 Volume:36 Page:1351-1362
ISSN:0354-5180
Container-title:Filomat
language:en
Short-container-title:Filomat

Author:

Ammous Basma¹,Dammak Lamia¹

Affiliation:

1. Faculty of Sciences, Department of Mathematics, Sfax, Tunisia

Abstract

The aim of this paper is to establish new transcendence criteria of p-adic continued fractions. We prove that a p-adic number whose sequence of partial quotients is bounded in Qp and begins with arbitrarily long palindromes is either quadratic or transcendental.

Publisher

National Library of Serbia

Subject

General Mathematics

Reference17 articles.

1. B. Adamczewski, J. P. Allouche, Reversals and palindromes in continued fractions, Theoretical Computer Science 380 (2007), 220-237.

2. B. Adamczewski, Y. Bugeaud, On the Littlewood conjecture in simultaneous Diophantine approximation, J. London Math. Soc 73 (2006) 355-366.

3. B. Adamczewski, Y. Bugeaud, Palindromic continued fractions, Ann. Inst. Fourier 57 (2007) 1557-1574.

4. B. Adamczewski, Y. Bugeaud, Transcendence criteria for pairs of continued fractions, G. Matematimaticki 41(61) (2006) 223-231.

5. L. Capuano, F. Veneziano, U. Zannier. An effective criterion for periodicity of ℓ-adic continued fractions, Math. Comp 88 (318) (2019) 1851-1882.

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1. On the Maillet–Baker Ruban Continued Fractions in the $$p$$-Adic Field;Mathematical Notes;2023-12

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