Journal
MATHEMATISCHE ANNALEN
Volume 383, Issue 1-2, Pages 645-698Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s00208-021-02232-4
Keywords
Vector valued Siegel cusp forms of half-integral weight; Metaplectic groups; Jacobi forms; Jacobi groups
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Funding
- JSPS Research Fellowships for Young Scientists KAKENHI [20J11779]
- Grants-in-Aid for Scientific Research [20J11779] Funding Source: KAKEN
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The study uses complex mathematical concepts and multiplicity formulas to prove Ibukiyama's conjectures on Siegel modular forms of half-integral weight and of degree 2, highlighting the significant role of representation theory of the Jacobi groups in the proof.
We prove Ibukiyama's conjectures on Siegel modular forms of half-integral weight and of degree 2 by using Arthur's multiplicity formula on the split odd special orthogonal group SO5 and Gan-Ichino's multiplicity formula on the metaplectic group Mp(4). In the proof, the representation theory of the Jacobi groups also plays an important role.
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