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Bugeaud, Yann, Budarina, Natalia, Dickinson, Detta and O'Donnell, Hugh (2011) On simultaneous rational approximation to a p-adic number and its integral powers. Proceedings of the Edinburgh Mathematical Society, 54 (3). pp. 599-612. ISSN 0013-0915
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Abstract
Let
p
be a prime number. For a positive integer
n
and a
p
-adic number
ξ
, let
λ
n
(
ξ
) denote
the supremum of the real numbers
λ
such that there are arbitrarily large positive integers
q
such that
qξ
p
,
qξ
2
p
,...,
qξ
n
p
are all less than
q
−
λ
−
1
. Here,
x
p
denotes the infimum of
|
x
−
n
|
p
as
n
runs
through the integers. We study the set of values taken by the function
λ
n
| Item Type: | Article |
|---|---|
| Keywords: | Diophantine approximation; Hausdorff dimension; p-adic number; |
| Academic Unit: | Faculty of Science and Engineering > Mathematics and Statistics |
| Item ID: | 4836 |
| Identification Number: | 10.1017/S001309151000060X |
| Depositing User: | Dr. Detta Dickinson |
| Date Deposited: | 19 Mar 2014 15:10 |
| Journal or Publication Title: | Proceedings of the Edinburgh Mathematical Society |
| Publisher: | Cambridge University Press (CUP) |
| Refereed: | Yes |
| Related URLs: | |
| URI: | https://mural.maynoothuniversity.ie/id/eprint/4836 |
| Use Licence: | This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here |
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