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A note on a problem of littlewood about diophantine approximation
Published online by Cambridge University Press: 26 February 2010
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A famous problem of Littlewood is whether or not inf u¬¬ux ¬¬u⬬=0, (1) for all real numbers α, β, where the infimum is taken over all positive integers u, and ¬¬ε¬¬, as usual, denotes the distance from ε to the nearest integer. By a well-known transference principle (see [2, p. 78], with an obvious modification), problem (1) is equivalent to whether or not inf ¬xy¬ ¬¬xx+y⬬=0 (2) for all real numbers α, β, with 1, α, β linearly independent over the rationals, where the infimum is taken over all non-zero integers x, y.
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- Copyright © University College London 1964
References
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