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arXiv · 2201.03986

Theta Series for Quadratic Forms of Signature $(n-1,1)$ with (Spherical) Polynomials II

Christina Roehrig·Sander Zwegers
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Abstract

We generalize the construction from arXiv:2102.09329 of theta series for quadratic forms of signature $(n-1,1)$ with homogeneous and spherical polynomials. Namely, we allow that the parameters $c_1,c_2$, which define the theta series and ensure the convergence of the defining series, are located on the boundary of the cone $C_Q$. This enables us to study several interesting examples such as Eisenstein series, modular forms on $\Gamma_0(4)$ which appear during the investigation of quadratic polynomials of a fixed discriminant, and a mock theta function of order 2 that is connected to the generating function of the Hurwitz class numbers $H(8n+7)$.

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Christina Roehrig, Sander Zwegers. 2022-01-11. Theta Series for Quadratic Forms of Signature $(n-1,1)$ with (Spherical) Polynomials II. https://arxiv.org/abs/2201.03986

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