TY - JOUR
T1 - Some metric properties of α-continued fractions
AU - Nakada, Hitoshi
AU - Natsui, Rie
N1 - Copyright:
Copyright 2004 Elsevier Science B.V., Amsterdam. All rights reserved.
PY - 2002/12/1
Y1 - 2002/12/1
N2 - The α-continued fraction is a modification of the nearest integer continued fractions taking n as the integer part of y when y ε [n - 1 + α, n + α), instead of the nearest integer. For x εo[α - 1, α), we have the following α-continued fraction expansion: with Cn ≥ 1 and εn = ±1 for n ≥ 1. We prove the Borel-Bernstein theorem for α-continued fractions and also discuss some metrical properties related to max1 ≤ n ≤ N Cn. Indeed, we prove that exist and have the same constant for almost every x.
AB - The α-continued fraction is a modification of the nearest integer continued fractions taking n as the integer part of y when y ε [n - 1 + α, n + α), instead of the nearest integer. For x εo[α - 1, α), we have the following α-continued fraction expansion: with Cn ≥ 1 and εn = ±1 for n ≥ 1. We prove the Borel-Bernstein theorem for α-continued fractions and also discuss some metrical properties related to max1 ≤ n ≤ N Cn. Indeed, we prove that exist and have the same constant for almost every x.
KW - Borel-Bernstein theorem
KW - Maxima of continued fraction coefficients
KW - α-Continued fractions
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U2 - 10.1016/S0022-314X(02)00008-2
DO - 10.1016/S0022-314X(02)00008-2
M3 - Article
AN - SCOPUS:0036913616
SN - 0022-314X
VL - 97
SP - 287
EP - 300
JO - Journal of Number Theory
JF - Journal of Number Theory
IS - 2
ER -