A Maass Lifting of ${\Theta }^3$ and Class Numbers of Real and imaginary Quadratic Fields

Robert C. Rhoades, Matthias Waldherr

We give an explicit construct of a harmonic weak Maass form $F_{\Theta }$ that is a "lift" of ${\Theta }^3$, where $\Theta$ is the classical Jacobi theta function. Just as the Fourier coefficients of $…