On a problem in simultaneous diophantine approximation: Littlewood's conjecture
نویسندگان
چکیده
منابع مشابه
On the Littlewood conjecture in simultaneous Diophantine approximation
For any given real number α with bounded partial quotients, we construct explicitly continuum many real numbers β with bounded partial quotients for which the pair (α, β) satisfies a strong form of the Littlewood conjecture. Our proof is elementary and rests on the basic theory of continued fractions.
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The Littlewood conjecture in Diophantine approximation claims that inf q≥1 q · ‖qα‖ · ‖qβ‖ = 0 holds for all real numbers α and β, where ‖ · ‖ denotes the distance to the nearest integer. Its p-adic analogue, formulated by de Mathan and Teulié in 2004, asserts that inf q≥1 q · ‖qα‖ · |q|p = 0 holds for every real number α and every prime number p, where | · |p denotes the p-adic absolute value ...
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ژورنال
عنوان ژورنال: Acta Mathematica
سال: 2000
ISSN: 0001-5962
DOI: 10.1007/bf02392812