The heat operator and mock Jacobi forms |
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Authors: | YoungJu Choie Subong Lim |
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Institution: | 1.Department of Mathematics and PMI,Pohang University of Science and Technology,Pohang,Korea |
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Abstract: | We study a necessary and sufficient condition for Jacobi integrals of weight
-r+\fracj2-r+\frac{j}{2}, r∈ℤ≥0, and index ℳ(j) on ℋ×ℂ
j
to have a dual Jacobi form of weight
r+\fracj2+2r+\frac{j}{2}+2 and index ℳ(j). Such a meromorphic Jacobi integral with a dual Jacobi form is called a mock Jacobi form whose concept was first introduced
by Zagier in Séminaire Bourbaki, 60éme année, 2006–2007, N° 986. In fact, we show the map Lr+1M(j)L^{r+1}_{\mathcal{M}^{(j)}} from the space of mock Jacobi forms to that of Jacobi forms is surjective by constructing the corresponding inverse image
via Eichler integral of vector valued modular forms which are coming from the theta decomposition of Jacobi forms. We discuss
Lerch sums as a typical example. |
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Keywords: | |
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