IRRATIONALITY MEASURES FOR CONTINUED FRACTIONS WITH ASYMPTOTIC CONDITIONS

被引：0

作者：

Hancl, Jaroslav ^{[1
,2
]}

Leppala, Kalle ^{[3
]}

机构：

[1] Univ Ostrava, Inst Res & Applicat Fuzzy Modeling, Dept Math, Fac Sci, 30 Dubna 22, CZ-70103 Ostrava 1, Czech Republic

[2] Univ Ostrava, Inst Res & Applicat Fuzzy Modeling, Ctr Excellence IT4Innovat, Div UO, 30 Dubna 22, CZ-70103 Ostrava 1, Czech Republic

[3] Aarhus Univ, Bioinformat Res Ctr, DK-8000 Aarhus C, Denmark

来源：

KYUSHU JOURNAL OF MATHEMATICS | 2016年 / 70卷 / 02期

基金：

芬兰科学院;

关键词：

continued fraction; Diophantine approximation; irrationality measure;

D O I：

10.2206/kyushujm.70.205

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We are interested in lower and upper bounds of asymptotic irrationality measures for certain simple continued fractions. A general procedure for estimation of real numbers by rational numbers is described. It is applied for simple continued fractions with quotients satisfying some asymptotic density conditions.

引用

页码：205 / 216

页数：12

共 20 条

[1] [Anonymous], 2006, An introduction to the theory of numbers
[2] BORWEIN J. M, 1987, A study in analytic number theory and computational complexity
[3] IRRATIONALITY MEASUREMENT FOR EA,A=0 RATIONAL OR LIOUVILLE NUMBER
BUNDSCHUH, P
[J]. MATHEMATISCHE ANNALEN, 1971, 192 (03) : 229 - +
[4] Bundschuh P., 1998, LITH MATH J, V38, p[19, 15]
[5] Irrationality measures for almost periodic continued fractions
Dodulikova, Silvia
Hancl, Jaroslav
Kolouch, Ondrej
Leinonen, Marko
Leppala, Kalle
[J]. GEORGIAN MATHEMATICAL JOURNAL, 2016, 23 (01) : 55 - 67
[6] Euler L., 1737, COMM ACAD SCI PETROP, V9, P98
[7] Euler L., OPERA OMNIA 1, VXIV, P186
[8] Fel'dman N.I., 1998, NUMBER THEORY 4, V44, P1
[9] SHARPENING OF BOUNDS ON CERTAIN LINEAR FORMS
GALOCHKIN, AI
[J]. MATHEMATICAL NOTES, 1976, 20 (1-2) : 575 - 581
[10] IRRATIONALITY MEASURES FOR CONTINUED FRACTIONS WITH ARITHMETIC FUNCTIONS
Hancl, Jaroslav
Leppala, Kalle
[J]. PUBLICATIONS DE L INSTITUT MATHEMATIQUE-BEOGRAD, 2015, 97 (111): : 139 - 148

← 1 2 →