Abstract
A conjecture on lifting to Siegel cusp forms of half-integral weight $k - 1/2$ of degree two from each pair of cusp forms of $SL_{2}(\mathbb{Z})$ of weight $2k - 2$ and $2k - 4$ is given with a conjectural relation of the $L$ functions and numerical evidences. We also describe the space of Siegel modular forms of half-integral weight, its “plus subspace” and Jacobi forms of degree two by explicitly given theta functions.
Citation
Shuichi Hayashida. Tomoyoshi Ibukiyama. "Siegel modular forms of half integral weight and a lifting conjecture." J. Math. Kyoto Univ. 45 (3) 489 - 530, 2005. https://doi.org/10.1215/kjm/1250281971
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