SIMULTANEOUS DIOPHANTINE APPROXIMATION BY SQUARE-FREE NUMBERS

Dietmann, Rainer

doi:10.1093/qmath/ham051

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SIMULTANEOUS DIOPHANTINE APPROXIMATION BY SQUARE-FREE NUMBERS

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Abstract

Let α₁, …,α_r ∈ R be ‘not very well approximable’, for example, Q-linearly independent real algebraic numbers. Then there are infinitely many positive square-free integers n such that ‖nα_i‖ << n^−(2/3r)+ϵ(1 ≤ i ≤ r), where ‖·‖ denotes distance to the nearest integer.

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SIMULTANEOUS DIOPHANTINE APPROXIMATION BY SQUARE-FREE NUMBERS

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SIMULTANEOUS DIOPHANTINE APPROXIMATION BY SQUARE-FREE NUMBERS

Abstract

Sign in

Personal account

Institutional access

Institutional account management

Get help with access

Institutional access

IP based access

Sign in through your institution

Sign in with a library card

Society Members

Sign in through society site

Sign in using a personal account

Personal account

Viewing your signed in accounts

Signed in but can't access content

Institutional account management

Purchase

Short-term Access

Rental

Citations

Views

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Latest

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