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Picard–Fuchs equation : ウィキペディア英語版 | Picard–Fuchs equation In mathematics, the Picard–Fuchs equation, named after Émile Picard and Lazarus Fuchs, is a linear ordinary differential equation whose solutions describe the periods of elliptic curves. ==Definition== Let : be the j-invariant with and the modular invariants of the elliptic curve in Weierstrass form: : Note that the ''j''-invariant is an isomorphism from the Riemann surface to the Riemann sphere ; where is the upper half-plane and is the modular group. The Picard–Fuchs equation is then : Written in Q-form, one has :
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「Picard–Fuchs equation」の詳細全文を読む
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