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

Badziahin D., Bugeaud Y., Schleischitz J.

Proceedings of the Edinburgh Mathematical Society, vol.64, no.2, pp.317-337, 2021 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 64 Issue: 2
  • Publication Date: 2021
  • Doi Number: 10.1017/s001309152100016x
  • Journal Name: Proceedings of the Edinburgh Mathematical Society
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Applied Science & Technology Source, MathSciNet, zbMATH
  • Page Numbers: pp.317-337
  • Keywords: simultaneous approximation, transference theorem, DIOPHANTINE APPROXIMATION
  • Middle East Technical University Affiliated: Yes

Abstract

Copyright © The Author(s), 2021. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society.Let be a prime number. For a positive integer and a real number, let denote the supremum of the real numbers for which there are infinitely many integer tuples such that are all less than, where is the maximum of. We establish new results on the Hausdorff dimension of the set of real numbers for which is equal to (or greater than or equal to) a given value.