On the Littlewood conjecture in simultaneous Diophantine approximation
نویسندگان
چکیده
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.
منابع مشابه
Around the Littlewood conjecture in Diophantine approximation
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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