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arXiv · 1106.0268

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

Robert C. Rhoades·Matthias Waldherr
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Abstract

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 "holomorphic part" of $F_Θ$ are associated to class numbers of real quadratic fields.

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Robert C. Rhoades, Matthias Waldherr. 2011-06-01. A Maass Lifting of $Θ^3$ and Class Numbers of Real and imaginary Quadratic Fields. https://arxiv.org/abs/1106.0268

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