Formal series of Jacobi forms
Hiroki Aoki, Tomoyoshi Ibukiyama, Cris Poor
TL;DR
This paper proves that formal series of scalar Jacobi forms with an involution condition converge for general paramodular levels, establishing their role as Fourier-Jacobi expansions of paramodular Fricke eigenforms.
Contribution
It demonstrates the convergence of formal Jacobi form series with involution conditions at general paramodular levels, linking them to Fourier-Jacobi expansions of eigenforms.
Findings
Formal series of scalar Jacobi forms converge under involution conditions
Convergence holds for general paramodular levels
Series represent Fourier-Jacobi expansions of Fricke eigenforms
Abstract
We prove for general paramodular level that formal series of scalar Jacobi forms with an involution condition necessarily converge and are therefore the Fourier-Jacobi expansions at the standard 1-cusp of paramodular Fricke eigenforms.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Algebra and Geometry · Advanced Topics in Algebra · Algebraic Geometry and Number Theory