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Lie Group Quantum Mathematics Seminar

Bounds for the constant terms of weight-0 vector-valued modular forms and generalized deep holes of the Leech lattice vertex operator algebra

Sven Moeller, Rutgers University

Location:  Hill 705
Date & time: Friday, 20 September 2019 at 12:00PM - 1:00PM

  • Abstract:  We derive an upper bound for (the sum corresponding to an isotropic subgroup of) the constant terms of a weight-0 vector-valued modular form that transforms under the Weil representation, based on a pairing argument with weight-2 vector-valued Eisenstein series.
  • As an application we prove a vertex algebra analogue of the remarkable result by Conway, Parker and Sloane (and Borcherds) that there is a bijection between the deep holes of the Leech lattice and the 23 Niemeier lattices with roots.

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