JournalsprimsVol. 48, No. 3pp. 579–613

Taylor Expansions of Jacobi Forms and Applications to Explicit Structures of Degree Two

  • Tomoyoshi Ibukiyama

    Osaka University Graduate School of Science, Japan
Taylor Expansions of Jacobi Forms and Applications to Explicit Structures of Degree Two cover
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Abstract

Natural mappings from the coecients of the Taylor expansion of Jacobi forms of general degree to products of certain spaces of vector valued Siegel modular forms are constructed. Proving surjectivity of these mappings in some special cases, we also clarify explicit structures of Jacobi forms of degree two of index one and of even weight of index two as modules over the graded ring of Siegel modular forms of even weight. We also prove surjectivity of the diagonal restriction of Jacobi forms of index one of degree two to the symmetric tensors of Jacobi forms of degree one.

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Tomoyoshi Ibukiyama, Taylor Expansions of Jacobi Forms and Applications to Explicit Structures of Degree Two. Publ. Res. Inst. Math. Sci. 48 (2012), no. 3, pp. 579–613

DOI 10.2977/PRIMS/82