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In mathematics, the Manin conjecture describes the conjectural distribution of rational points on an algebraic variety relative to a suitable height function. It was proposed by Yuri I. Manin and his collaborators〔 〕 in 1989 when they initiated a program with the aim of describing the distribution of rational points on suitable algebraic varieties. Their main conjecture is as follows. Let be a Fano variety defined over a number field , let be a height function which is relative to the anticanonical divisor and assume that is Zariski dense in . Then there exists a non-empty Zariski open subset such that the counting function of -rational points of bounded height, defined by : for , satisfies : as Here is the rank of the Picard group of and is a positive constant which later received a conjectural interpretation by Peyre. Manin's conjecture has been decided for special families of varieties,〔 〕 but is still open in general. == References == 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「Manin conjecture」の詳細全文を読む スポンサード リンク
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