Around the Littlewood conjecture in Diophantine approximation
نویسنده
چکیده
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 normalized by |p|p = p−1. We survey the known results on these conjectures and highlight recent developments.
منابع مشابه
On the Littlewood conjecture in simultaneous Diophantine approximation
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