Bugeaud, Yann and Budarina, Natalia and Dickinson, Detta and O'Donnell, Hugh
(2011)
On simultaneous rational approximation to a padic number and its integral powers.
Proceedings of the Edinburgh Mathematical Society, 54 (3).
pp. 599612.
ISSN 00130915
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
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