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In mathematics, the Littlewood conjecture is an open problem () in Diophantine approximation, proposed by John Edensor Littlewood around 1930. It states that for any two real numbers α and β, : where is here the distance to the nearest integer. ==Formulation and explanation== This means the following: take a point (α,β) in the plane, and then consider the sequence of points :(2α,2β), (3α,3β), ... . For each of these consider the closest lattice point, as determined by multiplying the distance to the closest line with integer x-coordinate by the distance to the closest line with integer y-coordinate. This product will certainly be at most 1/4. The conjecture makes no statement about whether this sequence of values will converge; it typically does not, in fact. The conjecture states something about the limit inferior, and says that there is a subsequence for which the distances decay faster than the reciprocal, i.e. :o(1/''n'') in the little-o notation. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Littlewood conjecture」の詳細全文を読む スポンサード リンク
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