Modular Solutions to Equations of Generalized Halphen Type

Details Modular Solutions to Equations of Generalized Halphen Type Modular Solutions to Equations of Generalized Halphen Type

1998-04-09

arxiv.org/abs/solv-int/9804006v3

Proc.Roy.Soc.Lond. 456 (2000) 261-294

Physics

High Energy Physics

High Energy Physics - Theory

PlainTeX 36gs. (Formula for Hecke operator corrected.)

Scientific paper

10.1098/rspa.2000.0517

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 $q$--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.

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