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2 results

  • The classification of free algebras of orthogonal modular forms

  • Part of
  • Haowu Wang
  • Journal:
    Compositio Mathematica / Volume 157 / Issue 9 / September 2021
    Published online by Cambridge University Press:
    06 August 2021, pp. 2026-2045
    Print publication:
    September 2021

  • We prove a necessary and sufficient condition for the graded algebra of automorphic forms on a symmetric domain of type IV being free. From the necessary condition, we derive a classification result. Let $M$ be an even lattice of signature $(2,n)$ splitting two hyperbolic planes. Suppose $\Gamma$ is a subgroup of the integral orthogonal group of $M$ containing the discriminant kernel. It is proved that there are exactly 26 groups $\Gamma$ such that the space of modular forms for $\Gamma$ is a free algebra. Using the sufficient condition, we recover some well-known results.

  • Theta constants associated to coverings of P1 branching at eight points

  • Keiji Matsumoto, Tomohide Terasoma
  • Journal:
    Compositio Mathematica / Volume 140 / Issue 5 / September 2004
    Published online by Cambridge University Press:
    04 December 2007, pp. 1277-1301
    Print publication:
    September 2004
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  • In this paper, we construct automorphic forms on the five-dimensional complex ball which give the inverse of the period map for cyclic 4-ple coverings of the complex projective line branching at eight points. We use theta constants associated to the Prym varieties of these coverings.