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Hausdorff Dimension for the Set of Points Connected with the Generalized Jarnik-Besicovitch Set

In this article we aim to investigate the Hausdorff dimension of the set of points x∈[0,1) such that for any r∈N

,
an+1(x)an+2(x)⋯an+r(x)≥eτ(x)(h(x)+⋯+h(Tn−1(x)))
holds for infinitely many n∈N , where h and τ are positive continuous functions, T is the Gauss map and an(x) denotes the nth partial quotient of x in its continued fraction expansion. By appropriate choices of r,τ(x) and h(x) we obtain various classical results including the famous Jarník–Besicovitch theorem.

Ketersediaan

Informasi Detail

Judul Seri

JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY; Vol.112 Issue.1 February 2022

No. Panggil

-

Penerbit

: .,

Deskripsi Fisik

p. 1-29

Bahasa

English

ISBN/ISSN

-

Klasifikasi

NONE

Tipe Isi

-

Tipe Media

-

Tipe Pembawa

-

Edisi

-

Subjek

CONTINUED FRACTIONS
HAUSDORFF DIMENSION
JARNIK-BESICOVITCH THEOREM

Info Detail Spesifik

DOI: https://doi.org/10.1017/S1446788720000464

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Ayreena Bakhtawar

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