Weight One Jacobi Forms and Umbral Moonshine

Abstract

We analyze holomorphic Jacobi forms of weight one with level. One such form plays an important role in umbral moonshine, leading to simplifications of the statements of the umbral moonshine conjectures. We prove that non-zero holomorphic Jacobi forms of weight one do not exist for many combinations of index and level, and use this to establish a characterization of the McKay--Thompson series of umbral moonshine in terms of Rademacher sums.

41 pages, 39 tables

Cited by in corpus (7)

• Super Vertex Algebras, Meromorphic Jacobi Forms and Umbral Moonshine
• A Borcherds-Kac-Moody superalgebra with Conway symmetry
• Supersingular Elliptic Curves and Moonshine
• Attractive Strings and Five-Branes, Skew-Holomorphic Jacobi Forms and Moonshine
• Symmetries of Calabi-Yau Prepotentials with Isomorphic Flops
• Umbral Moonshine and String Duality
• TASI Lectures on Moonshine