2013/03/15 by Jan Hendrik Bruinier, Bruinier, Jan Hendrik
Mathematics · #11F46 #11F50 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Number Theory (math.NT) #math.NT #msc:11F46 #msc:11F50
paper · pdf · doi:10.48550/arxiv.1303.3699
8 pages, more details on Kudla's modularity conjecture included, reference added
openalex publication_date 2013/03/15 · arxiv created 2014/08/22 · arxiv updated 2014/08/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
H. Aoki showed that any symmetric formal Fourier-Jacobi series for the symplectic group Sp2(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.