Weight one Jacobi forms and umbral moonshine.

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 nonzero 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. [ABSTRACT FROM AUTHOR]