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

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

We give an explicit construct of a harmonic weak Maass form F Θ 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 …