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Lithuanian Mathematical Journal

, Volume 59, Issue 1, pp 131–141 | Cite as

On the simultaneous rational approximations to real and p-adic numbers

  • Vilius StakėnasEmail author
Article
  • 26 Downloads

Abstract

We consider simultaneous rational approximations to real and p-adic numbers. We prove that for any irrational number α0 and p-adic number α, there are infinitely many irreducible fractions satisfying ∣α0 − m/n ∣  < 1/n2/3 − ∈ and |α0 − m/n|p < 1/n2/3 − ∈, where ∈ > 0 is an arbitrary number, and ∣ ⋅  ∣ p is the p-adic norm.

Keywords

p-adic numbers rational approximations 

MSC

11J13 11J61 

Notes

References

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Institute of Computer ScienceVilnius UniversityVilniusLithuania

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