2017/12/31 by Ehud de Shalit, Ehud De Shalit, Eyal Z. Goren · 10 citations
Mathematics · #Advanced Algebra and Geometry #Algebra over a field #Algebraic Geometry and Number Theory #Field (mathematics) #Geometry #Geometry and complex manifolds #Hilbert space #Mathematics #Modular design #Modular form #Operator (biology) #Pure mathematics #Quadratic equation #Quadratic field #Quadratic function #Scalar (mathematics) #Shimura variety #Signature (topology) #Unitary operator #Unitary state #math.AG #math.NT #msc:11G18 #msc:14G35
paper · pdf · doi:10.2140/ant.2019.13.1829
published in Algebra & Number Theory 13(8), 1829-1877 (Mathematical Sciences Publishers) · 46 pages
arxiv created 2019/06/14 · openalex publication_date 2019/10/09 · arxiv updated 2019/10/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We define a theta operator on [math] -adic vector-valued modular forms on unitary groups of arbitrary signature, over a quadratic imaginary field in which [math] is inert. We study its effect on Fourier–Jacobi expansions and prove that it extends holomorphically beyond the [math] -ordinary locus, when applied to scalar-valued forms.