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    On simultaneous rational approximation to a p-adic number and its integral powers


    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:

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