论文标题
theta系列的二次形式签名$（n-1,1）$带（球形）多项式II
Theta Series for Quadratic Forms of Signature $(n-1,1)$ with (Spherical) Polynomials II
论文作者
论文摘要
我们从theta系列的Arxiv：2102.09329的构造中概括了二次形式的签名$（n-1,1）$，具有同质和球形多项式。也就是说，我们允许定义theta系列并确保定义系列的汇聚的参数$ C_1，C_2 $位于圆锥$ C_Q $的边界上。这使我们能够研究几个有趣的例子，例如Eisenstein系列，$γ_0（4）$的模块化形式，这些形式在研究固定判别的二次多项式时出现，以及与Hurwitz类数字$ H（8n+7）$相关的订单2的模拟THETA函数。
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 $Γ_0(4)$ 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 $H(8n+7)$.
