## Vector valued formal Fourier-Jacobi series

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- by Jan Hendrik Bruinier PDF
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**143**(2015), 505-512 Request permission

## Abstract:

H. Aoki showed that any symmetric formal Fourier-Jacobi series for the symplectic group $\mathrm {Sp}_2(\mathbb {Z})$ is the Fourier-Jacobi expansion of a holomorphic Siegel modular form. We prove an analogous result for vector valued symmetric formal Fourier-Jacobi series, by combining Aoki’s theorem with facts about vector valued modular forms. Recently, this result was also proved independently by M. Raum using a different approach. As an application, by means of work of W. Zhang, modularity results for special cycles of codimension $2$ on Shimura varieties associated to orthogonal groups can be derived.## References

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## Additional Information

**Jan Hendrik Bruinier**- Affiliation: Fachbereich Mathematik, Technische Universität Darmstadt, Schlossgartenstrasse 7, D–64289 Darmstadt, Germany
- MR Author ID: 641446
- Email: bruinier@mathematik.tu-darmstadt.de
- Received by editor(s): March 15, 2013
- Received by editor(s) in revised form: May 16, 2013
- Published electronically: September 19, 2014
- Additional Notes: The author was partially supported by DFG grants BR-2163/2-2 and FOR 1920.
- Communicated by: Kathrin Bringmann
- © Copyright 2014 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**143**(2015), 505-512 - MSC (2010): Primary 11F46, 11F50
- DOI: https://doi.org/10.1090/S0002-9939-2014-12272-6
- MathSciNet review: 3283640