Continued fractions arising from<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:msub><mml:mrow><mml:mi mathvariant="script">F</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:math>

Sarma, Ritumoni; Kushwaha, Seema; Krishnan, Ravikiran

doi:10.1016/j.jnt.2015.02.010

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Cited by 9 publications

(10 citation statements)

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“…Then, Deger et al prove that a shortest path in trees of these suborbital graphs is a special case of Pringsheim continued fraction [7]. The main important development is revealed by Sarma et al [21]. The authors shows that the subgraph F 1,2 can be defined as a new kind of continued fraction and any irrational numbers has a unique F 1,2 expansion.…”

Section: Discussionmentioning

confidence: 99%

Suborbital Graphs of the Normalizer of Modular Group in the Picard Group

Gözütok

Güler

2017

Iran J Sci Technol Trans Sci

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Section: Discussionmentioning

confidence: 99%

Suborbital Graphs of the Normalizer of Modular Group in the Picard Group

Gözütok

Güler

2017

Iran J Sci Technol Trans Sci

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“…The graph F u,N is connected exactly for N ≤ 4, and it is a tree exactly for N = 2, 4. Using the graph F 1,2 and F 1,3 , we have constructed continued fractions called F 1,2 -continued fractions [7] and F 1,3 -continued fractions [4], respectively. The graphs F u,N and F N −u,N are isomorphic under the map v → −v for each vertex v of F u,N .…”

Section: Introductionmentioning

confidence: 99%

Farey-subgraphs and Continued Fractions

Kushwaha¹,

Sarma²

2021

Preprint

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In this note, we study a family of subgraphs of the Farey graph, denoted as F N for every N ∈ N. We show that F N is connected if and only if N is either equal to one or a prime power. We introduce a class of continued fractions referred to as F N -continued fractions for each N > 1. We establish a relation between F N -continued fractions and certain paths from infinity in the graph F N . We discuss existence and uniqueness of F N -continued fraction expansions of real numbers.

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“…Elliptic elements do not necessarily correspond to circuits of the same order. On the other hand, it is worth noting that these graphs give some number theoretical results about continued fractions and Fibonacci numbers as in [4,8,17].…”

Section: Introductionmentioning

confidence: 99%