On Diophantine approximations of Ramanujan type q-continued fractions

被引：6

作者：

Matala-aho, Tapani ^{[1
]}

Merila, Ville ^{[1
]}

机构：

[1] Oulun Yliopisto, Matematiikan Laitos, Oulu 90014, Finland

来源：

JOURNAL OF NUMBER THEORY | 2009年 / 129卷 / 05期

关键词：

Irrationality measure; q-Continued fraction; q-Series; Q-DIFFERENCE EQUATIONS; Q-SERIES; VALUES;

D O I：

10.1016/j.jnt.2008.06.017

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We shall consider arithmetical properties of the q-continued fractions K-n=1(infinity) q(sn)(S-0 + S(1)q(n) + ... + S(h)q(hn))/T-0 + T(1)q(n) + . . . + T(l)q(ln), S-i, T-i, q is an element of K, vertical bar q vertical bar(v) < 1, and some related continued fractions where v is a fixed valuation of an algebraic number field 165 and s, h, l is an element of N. In particular, we get sharp irrationality measures for certain Ramanujan, Ramanujan-Selberg, Eisenstein and Tasoev continued fractions. (C) 2009 Elsevier Inc. All rights reserved.

引用

页码：1044 / 1055

页数：12

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