2010/12/31 by Charles H. Conley, Martin Raum, Martin Westerholt-Raum
Mathematics · #Advanced Algebra and Geometry #Degree (music) #Extension (predicate logic) #Geometry and complex manifolds #Harmonic #Homotopy and Cohomology in Algebraic Topology #Operator (biology) #Order (exchange) #Rank (graph theory) #math.NT #math.RT #msc:11F50 #msc:17B10 #msc:22E47
paper · pdf · doi:10.1142/s1793042116501165
published as Int. J. Number Theory 12 (2016), no. 7, 1871-1897 · 28 pages
arxiv created 2015/01/23 · openalex publication_date 2015/11/01 · openalex created_date 2016/06/24 · arxiv updated 2019/01/01 · openalex updated_date 2026/08/05
We define and investigate real analytic weak Jacobi forms of degree 1 and arbitrary rank. En route we calculate the Casimir operator associated to the maximal central extension of the real Jacobi group, which for rank exceeding 1 is of order 4. In ranks exceeding 1, the notions of H-harmonicity and semi-holomorphicity are the same.