Classification of the space spanned  by theta series and applications

Choie, YoungJu; Richter, Olav K.

doi:10.1090/s0002-9939-07-08706-0

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Lifting Of Modular Forms To Jacobi Forms1

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2012

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“…where det (−iZ) 1 2 is positive if Z = iY for positive definite Y ∈ R (2,2) (see [6] for a simple proof of (15) that does not require Poisson summation). Now we will regard θ µ (τ, z) as a special case of Θ M (Z, W ).…”

Section: Lifting Of Modular Forms To Jacobi Formsmentioning

confidence: 99%

Jacobi forms over complex quadratic fields via the cubic Casimir operators

Bringmann

Conley²,

Richter

2012

Comment. Math. Helv.

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We dedicate this article to Harold Stark on the occasion of his 70 th birthday.Abstract. We prove that the center of the algebra of differential operators invariant under the action of the Jacobi group over a complex quadratic field is generated by two cubic Casimir operators, which we compute explicitly. In the spirit of Borel, we consider Jacobi forms over complex quadratic fields that are also eigenfunctions of these Casimir operators, a new approach in the complex case. Theta functions and Eisenstein series provide standard examples. In addition, we introduce an analog of Kohnen's plus space for modular forms of half-integral weight over K = Q(i), and provide a lift from it to the space of Jacobi forms over K = Q(i).

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Section: Lifting Of Modular Forms To Jacobi Formsmentioning

confidence: 99%