Theta lifts for Lorentzian lattices and coefficients of mock theta functions
arXiv:1912.08126 · doi:10.1007/s00209-020-02572-y
Abstract
We evaluate regularized theta lifts for Lorentzian lattices in three different ways. In particular, we obtain formulas for their values at special points involving coefficients of mock theta functions. By comparing the different evaluations, we derive recurrences for the coefficients of mock theta functions, such as Hurwitz class numbers, Andrews' spt-function, and Ramanujan's mock theta functions.
24 pages
References in corpus (5)
- Eichler-Selberg Type Identities for Mixed Mock Modular Forms
- Algebraic and transcendental formulas for the smallest parts function
- Elliptic curves, modular forms, and sums of Hurwitz class numbers
- CM values of regularized theta lifts and harmonic weak Maaß forms of weight one
- Completions and algebraic formulas for the coefficients of Ramanujan's mock theta functions