Bugeaud, Yann and Budarina, Natalia and 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:	https://doi.org/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
URI:	Publisher
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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