Slow-Growing Weak Jacobi Forms

Abstract: Weak Jacobi forms of weight 0 can be exponentially lifted to meromorphic Siegel paramodular forms. It was recently observed that the Fourier coefficients of such lifts are then either fast growing or slow growing. Those weak Jacobi forms with slow growing behavior could describe the elliptic genus of a CFT whose symmetric orbifold exhibits a slow supergravity-like growth. In this talk, we investigate the space of weak Jacobi forms that lead to slow growth. We provide analytic and numerical evidence for the conjecture that there are such slow growing forms for any index.

number theory

Audience: researchers in the topic

University of Arizona Algebra and Number Theory Seminar