Hurwitz类数关系与 mock 模形式
Hurwitz class number relations and mock modular forms
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中文总结 AI 辅助
本文将Hurwitz经典类数关系推广，以正定二元二次型替代一元二次型，建立涉及Cohen广义类数的无穷族类数关系，并构造依赖亏格的降阶算子。
中文摘要 AI 辅助
Hurwitz的经典类数关系表达了一元theta函数与类数生成函数乘积的傅里叶系数。本文中，我们通过将一元二次型$m^2$替换为正定二元二次型，建立了无穷族类似类数关系，这些恒等式涉及Cohen广义类数，且仅依赖于基础二次型的亏格；为此，我们构造了依赖亏格的降阶算子。
英文摘要
A classical class number relation of Hurwitz expresses the Fourier coefficients of the product of a unary theta function and the class number generating function. Here, we establish an infinite family of analogous class number relations obtained by replacing the unary quadratic form $m^2$ by positive-definite binary quadratic forms. These identities involve Cohen's generalized class numbers and depend only on the genus of the underlying quadratic form. For this, we construct a genus-dependent level-lowering operator.
