Almost harmonic Maass forms and Kac-Wakimoto characters

Abstract: We explain the modular properties of certain characters due to Kac and Wakimoto pertaining to $sl(m|n)^{}$, where n is a positive integer. We prove that these characters are essentially holomorphic parts of new automorphic objects we call "almost harmonic Maass forms," which generalize both harmonic Maass forms and almost holomorphic modular forms. By using new methods involving meromorphic Jacobi forms, this generalizes prior works of Bringmann-Ono and Bringmann-Folsom, which treat the case n=1. This is joint work with Kathrin Bringmann (University of Cologne).

number theory

Audience: researchers in the topic

EIMI Number Theory Seminar

Series comments: Password: the number of quadratic nonresidues modulo 23