Siegel modular forms of weight 13 and the Leech lattice

  • Gaëtan Chenevier

    Université Paris-Saclay, Orsay, France
  • Olivier Taïbi

    École Normale Supérieure de Lyon, France
Siegel modular forms of weight 13 and the Leech lattice cover

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Abstract

For and , there is a nonzero alternating -multilinear form on the lattice, unique up to a scalar, which is invariant by the orthogonal group of . The harmonic Siegel theta series built from these alternating forms are Siegel modular cuspforms of weight for . We prove that they are nonzero eigenforms, determine one of their Fourier coefficients, and give informations about their standard -functions. These forms are interesting since, by a recent work of the authors, they are the only nonzero Siegel modular forms of weight for , for any .

Cite this article

Gaëtan Chenevier, Olivier Taïbi, Siegel modular forms of weight 13 and the Leech lattice. Enseign. Math. 68 (2022), no. 1/2, pp. 61–98

DOI 10.4171/LEM/1021