Contents Online
Mathematical Research Letters
Volume 18 (2011)
Number 5
A Maass Lifting of $\Theta^3$ and Class Numbers of Real and imaginary Quadratic Fields
Pages: 1001 – 1012
DOI: https://dx.doi.org/10.4310/MRL.2011.v18.n5.a17
Authors
Abstract
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 $\Theta^3$ are related to class numbers of imaginary quadratic fields, the Fourier coefficients of the “holomorphic part” of $F_{\Theta}$ are associated to class numbers of real quadratic fields.
Published 28 October 2011