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Theta Series for Quadratic Forms of Signature $(n-1,1)$ with (Spherical) Polynomials II
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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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Cited by 1 Pith paper
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Indefinite theta functions arising from affine Lie superalgebras and sums of triangular numbers
New families of q-series identities for powers of the generating function of triangular numbers are proved via indefinite theta functions and affine Lie superalgebra denominator identities.
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