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In mathematics, modular symbols, introduced independently by Bryan John Birch and by , span a vector space closely related to a space of modular forms, on which the action of the Hecke algebra can be described explicitly. This makes them useful for computing with spaces of modular forms. ==Definition== The abelian group of (universal weight 2) modular symbols is spanned by symbols for α, β in the rational projective line Q∪ ∞ subject to the relations * + = Informally, represents a homotopy class of paths from α to β in the upper half-plane. The group ''GL''2(Q) acts on the rational projective line, and this induces an action on the modular symbols. There is a pairing between cusp forms ''f'' of weight 2 and modular symbols given by integrating the cusp form, or rather ''fd''τ, along the path corresponding to the symbol. 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「Modular symbol」の詳細全文を読む スポンサード リンク
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