论文标题
分隔函数和正交状态的探索和探索的符号猜想
Symplectic conjectures for sums of divisor functions and explorations of an orthogonal regime
论文作者
论文摘要
在[arxiv：2107.01437]中，作者研究了函数字段上的某些总和$ d_k（f）$的均值Roditty-Gershon和Rudnick [Arxiv：1504.07804]用于单一矩阵。我们提出了一个类似的问题，该问题在正交矩阵的集合上产生了不可或缺的问题，并对符号和正交矩阵积分进行了更详细的研究，将它们与对称函数理论有关。功能字段结果导致有关数字字段上类似问题的猜想。
In [arXiv:2107.01437], the authors studied the mean-square of certain sums of the divisor function $d_k(f)$ over the function field $\mathbb{F}_q[T]$ in the limit as $q \to \infty$ and related these sums to integrals over the ensemble of symplectic matrices, along similar lines as previous work of Keating, Rodgers, Roditty-Gershon and Rudnick [arXiv:1504.07804] for unitary matrices. We present an analogous problem yielding an integral over the ensemble of orthogonal matrices and pursue a more detailed study of both the symplectic and orthogonal matrix integrals, relating them to symmetric function theory. The function field results lead to conjectures concerning analogous questions over number fields.
