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

• 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. In ranks exceeding 1, the notions of H-harmonicity and semi-holomorphicity are the same.

Ämnesord

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Nyckelord

Semi-holomorphic Jacobi forms

skew-holomorphic Jacobi forms

invariant differential operators

xi-

complex quadratic fields

casimir-operators

modular-forms

Mathematics

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