数学物理学报(英文版) ›› 2016, Vol. 36 ›› Issue (1): 257-264.doi: 10.1016/S0252-9602(15)30093-X
ON POINTS CONTAIN ARITHMETIC PROGRESSIONS IN THEIR LÜROTH EXPANSION
张振亮1,2, 曹春云3
- 1. School of Mathematical Sciences, Henan Institute of Science and Technology, Xinxiang 453003, China;
2. School of Mathematics and Statistics, Huazhong Universitry of Science and Technology, Wuhan 430074, China;
3. College of Science, Huazhong Agricultural Universitry, Wuhan 430070, China
ON POINTS CONTAIN ARITHMETIC PROGRESSIONS IN THEIR LÜROTH EXPANSION
Zhenliang ZHANG1,2, Chunyun CAO3
- 1. School of Mathematical Sciences, Henan Institute of Science and Technology, Xinxiang 453003, China;
2. School of Mathematics and Statistics, Huazhong Universitry of Science and Technology, Wuhan 430074, China;
3. College of Science, Huazhong Agricultural Universitry, Wuhan 430070, China
摘要：
For any x∈(0, 1](except at most countably many points), there exists a unique sequence {dn(x)}n≥1 of integers, called the digit sequence of x, such that
x=
1/(d1(x)(d1(x)-1)…dj-1(x)(dj-1(x)-1)dj(x))
.The dexter infinite series expansion is called the Lüroth expansion of x.This paper is concerned with the size of the set of points x whose digit sequence in its Lüroth expansion is strictly increasing and contains arbitrarily long arithmetic progressions with arbitrary common difference.More precisely, we determine the Hausdorff dimension of the above set.
中图分类号:
- 11K55