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2 results

  • Some constructions of modular forms for the Weil representation of SL2(ℤ)

  • Nils R. Scheithauer
  • Journal:
    Nagoya Mathematical Journal / Volume 220 / December 2015
    Published online by Cambridge University Press:
    11 January 2016, pp. 1-43
    Print publication:
    December 2015
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  • Modular forms for the Weil representation of SL2 (ℤ) play an important role in the theory of automorphic forms on orthogonal groups. In this paper we give some explicit constructions of these functions. As an application, we construct new examples of generalized Kac-Moody algebras whose denominator identities are holomorphic automorphic products of singular weight. They correspond naturally to the Niemeier lattices with root systems and to the Leech lattice.

  • On generalized theta series liftings

  • Part of
  • Min Ho Lee
  • Journal:
    Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics / Volume 62 / Issue 2 / April 1997
    Published online by Cambridge University Press:
    09 April 2009, pp. 229-238
    Print publication:
    April 1997
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  • We generalize dual reductive pairs by using reductive groups that are not necessarily subgroups of symplectic groups and construct the corresponding theta-series liftings for certain types of automorphic forms. We also discuss connections of such generalized theta-series liftings with families of abelian varieties parametrized by an arithmetic variety.