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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Vector valued formal Fourier-Jacobi series
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by Jan Hendrik Bruinier PDF
Proc. Amer. Math. Soc. 143 (2015), 505-512 Request permission


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.
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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:
  • 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:
  • MathSciNet review: 3283640