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.
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Stakėnas, V. On the simultaneous rational approximations to real and p-adic numbers. Lith Math J 59, 131–141 (2019). https://doi.org/10.1007/s10986-019-09426-z
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DOI: https://doi.org/10.1007/s10986-019-09426-z