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- Modular_equation abstract "In mathematics, a modular equation is an algebraic equation satisfied by moduli, in the sense of moduli problem. That is, given a number of functions on a moduli space, a modular equation is an equation holding between them, or in other words an identity for moduli.The most frequent use of the term modular equation is in relation to the moduli problems for elliptic curves. In that case the moduli space itself is of dimension one. That implies that any two rational functions F and G, in the function field of the modular curve, will satisfy a modular equation P(F,G) = 0 with P a non-zero polynomial of two variables over the complex numbers. For suitable non-degenerate choice of F and G, the equation P(X,Y) = 0 will actually define the modular curve. This can be qualified by saying that P, in the worst case, will be of high degree and the plane curve it defines will have singular points; and the coefficients of P may be very large numbers. Further, the 'cusps' of the moduli problem, which are the points of the modular curve not corresponding to honest elliptic curves but degenerate cases, may be difficult to read off from knowledge of P.In that sense a modular equation becomes the equation of a modular curve. Such equations first arose in the theory of multiplication of elliptic functions (geometrically, the n2-fold covering map from a 2-torus to itself given by the mapping x → n·x on the underlying group) expressed in terms of complex analysis.".
- Modular_equation wikiPageID "439154".
- Modular_equation wikiPageLength "1850".
- Modular_equation wikiPageOutDegree "18".
- Modular_equation wikiPageRevisionID "677960259".
- Modular_equation wikiPageWikiLink Algebraic_equation.
- Modular_equation wikiPageWikiLink Category:Modular_forms.
- Modular_equation wikiPageWikiLink Coefficient.
- Modular_equation wikiPageWikiLink Complex_analysis.
- Modular_equation wikiPageWikiLink Complex_number.
- Modular_equation wikiPageWikiLink Covering_map.
- Modular_equation wikiPageWikiLink Covering_space.
- Modular_equation wikiPageWikiLink Elliptic_curve.
- Modular_equation wikiPageWikiLink Elliptic_function.
- Modular_equation wikiPageWikiLink Function_field_of_an_algebraic_variety.
- Modular_equation wikiPageWikiLink Identity_(mathematics).
- Modular_equation wikiPageWikiLink Mathematical_singularity.
- Modular_equation wikiPageWikiLink Mathematics.
- Modular_equation wikiPageWikiLink Moduli_problem.
- Modular_equation wikiPageWikiLink Moduli_space.
- Modular_equation wikiPageWikiLink Polynomial.
- Modular_equation wikiPageWikiLink Ramanujans_lost_notebook.
- Modular_equation wikiPageWikiLink Rational_function.
- Modular_equation wikiPageWikiLink Singularity_(mathematics).
- Modular_equation wikiPageWikiLink Torus.
- Modular_equation wikiPageWikiLinkText "Modular equation".
- Modular_equation wikiPageWikiLinkText "modular equation".
- Modular_equation hasPhotoCollection Modular_equation.
- Modular_equation wikiPageUsesTemplate Template:Unreferenced.
- Modular_equation subject Category:Modular_forms.
- Modular_equation hypernym Equation.
- Modular_equation type Article.
- Modular_equation type Article.
- Modular_equation comment "In mathematics, a modular equation is an algebraic equation satisfied by moduli, in the sense of moduli problem. That is, given a number of functions on a moduli space, a modular equation is an equation holding between them, or in other words an identity for moduli.The most frequent use of the term modular equation is in relation to the moduli problems for elliptic curves. In that case the moduli space itself is of dimension one.".
- Modular_equation label "Modular equation".
- Modular_equation sameAs m.028n8y.
- Modular_equation sameAs Q6889716.
- Modular_equation sameAs Q6889716.
- Modular_equation wasDerivedFrom Modular_equation?oldid=677960259.
- Modular_equation isPrimaryTopicOf Modular_equation.