Harmonic Maaß-Jacobi forms of degree 1 with higher rank indices

Details Harmonic Maaß-Jacobi forms of degree 1 with higher rank indices Harmonic Maaß-Jacobi forms of degree 1 with higher rank indices

2010-12-13

arxiv.org/abs/1012.2897v1

Mathematics

Number Theory

29 pages

Scientific paper

We define and investigate real analytic weak Jacobi forms of degree 1 and arbitrary rank. En route we calculate the Casimir operator associated to the maximal central extension of the real Jacobi group, which for rank exceeding 1 is of order 4. The notion of mixed mock modular forms is extended to Jacobi forms so as to include multivariable Appell functions in a natural way. Using the Casimir operator, we make a connection between this new notion and the notion of real analytic Jacobi forms.

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