A maass lifting of Θ ~3 and class numbers of real and imaginary quadratic fields

摘要

We give an explicit construct of a harmonic weak Maass form FΘ that is a "lift" of Θ ~3, where Θ is the classical Jacobi theta function. Just as the Fourier coefficients of Θ ~3 are related to class numbers of imaginary quadratic fields, the Fourier coefficients of the "holomorphic part" of FΘ are associated to class numbers of real quadratic fields.