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In mathematics, the Sato–Tate conjecture is a statistical statement about the family of elliptic curves ''Ep'' over the finite field with ''p'' elements, with ''p'' a prime number, obtained from an elliptic curve ''E'' over the rational number field, by the process of reduction modulo a prime for almost all ''p''. If ''Np'' denotes the number of points on ''Ep'' and defined over the field with ''p'' elements, the conjecture gives an answer to the distribution of the second-order term for ''Np''. That is, by Hasse's theorem on elliptic curves we have : as ''p'' → ∞, and the point of the conjecture is to predict how the O-term varies. ==Statement== Define ''θ''''p'' as the solution to the equation : Let ''E'' be an elliptic curve without complex multiplication. Then, for every two real numbers and for which , : 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「Sato–Tate conjecture」の詳細全文を読む スポンサード リンク
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