5 research outputs found

    Modular Solutions to Equations of Generalized Halphen Type

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    Solutions to a class of differential systems that generalize the Halphen system are determined in terms of automorphic functions whose groups are commensurable with the modular group. These functions all uniformize Riemann surfaces of genus zero and have qq--series with integral coefficients. Rational maps relating these functions are derived, implying subgroup relations between their automorphism groups, as well as symmetrization maps relating the associated differential systems.Comment: PlainTeX 36gs. (Formula for Hecke operator corrected.

    The Ising model: from elliptic curves to modular forms and Calabi–Yau equations

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    A Threefold Model of Intellectual Styles

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