On the diophantine properties of λ-expansions
Persson, Tomas LU
and Reeve, Henry
(2013)
In Mathematika
59(1).
p.65-86
- Abstract
- For and α, we consider sets of numbers x such that for infinitely many n, x is 2−αn -close to some ∑ n i=1 ω i λ i , where ω i ∈{0,1}. These sets are in Falconer’s intersection classes for Hausdorff dimension s for some s such that −(1/α)(log λ /log 2 )≤s≤1/α. We show that for almost all , the upper bound of s is optimal, but for a countable infinity of values of λ the lower bound is the best possible result.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/3233422
- author
- Persson, Tomas
LU
and Reeve, Henry
- organization
- publishing date
- 2013
- type
- Contribution to journal
- publication status
- published
- subject
- in
- Mathematika
- volume
- 59
- issue
- 1
- pages
- 65 - 86
- publisher
- John Wiley & Sons Inc.
- external identifiers
-
- wos:000327271600005
- scopus:84872196241
- ISSN
- 0025-5793
- DOI
- 10.1112/S0025579312001076
- language
- English
- LU publication?
- yes
- id
- 218d5c9e-7c2e-4665-9a59-7e0351ef8429 (old id 3233422)
- alternative location
- https://arxiv.org/abs/1202.4904
- date added to LUP
- 2016-04-01 11:01:34
- date last changed
- 2025-12-04 14:16:59
@article{218d5c9e-7c2e-4665-9a59-7e0351ef8429,
abstract = {{For and α, we consider sets of numbers x such that for infinitely many n, x is 2−αn -close to some ∑ n i=1 ω i λ i , where ω i ∈{0,1}. These sets are in Falconer’s intersection classes for Hausdorff dimension s for some s such that −(1/α)(log λ /log 2 )≤s≤1/α. We show that for almost all , the upper bound of s is optimal, but for a countable infinity of values of λ the lower bound is the best possible result.}},
author = {{Persson, Tomas and Reeve, Henry}},
issn = {{0025-5793}},
language = {{eng}},
number = {{1}},
pages = {{65--86}},
publisher = {{John Wiley & Sons Inc.}},
series = {{Mathematika}},
title = {{On the diophantine properties of λ-expansions}},
url = {{http://dx.doi.org/10.1112/S0025579312001076}},
doi = {{10.1112/S0025579312001076}},
volume = {{59}},
year = {{2013}},
}