过划分$M2$ -秩差、类数关系和向量值模拟爱森斯坦级数
Overpartition $M2$-rank differences, class number relations, and vector-valued mock Eisenstein series
摘要：
我们证明了过划分$M2$秩差的生成函数是，直到系数符号，一个组件的向量值模拟爱森斯坦系列附加到一定的二次型。我们用它来计算类似的类数关系的$M2$秩差。作为应用，我们将克罗内克-赫维茨关系分成“偶数”和“奇数”部分，并计算形式为$\sum_{r \in \mathbb{Z}} H(n - 2r^2)$的赫维茨类数的和。
英文摘要：
We prove that the generating function of overpartition $M2$-rank differences is, up to coefficient signs, a component of the vector-valued mock Eisenstein series attached to a certain quadratic form. We use this to compute analogs of the class number relations for $M2$-rank differences. As applications we split the Kronecker-Hurwitz relation into its "even" and "odd" parts and calculate sums over Hurwitz class numbers of the form $\sum_{r \in \mathbb{Z}} H(n - 2r^2)$.
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