论文标题
扩展，分裂性和平价：解释
Expansion, divisibility and parity: an explanation
论文作者
论文摘要
在看到有关质量分解分布的问题如何（直到最近才无法访问）的质疑是如何限制了在描述分解的图表上定义的操作员的规范之后，我们将展示如何绑定该规范。从本质上讲，该图是一个强大的局部扩展器，所有特征值都以恒定因素为界的理论最小值（即，与Ramanujan图相对应的特征值结合）。证明将使我们踏上从图理论到线性代数以及数字的几何形状，再到图理论的几何形状，并通过一般的筛子辅助。这是一张说明书；完整的证明已作为M. radziwi \ {l} \ {l}的关节预印本。
After seeing how questions on the finer distribution of prime factorization -- considered inaccessible until recently -- reduce to bounding the norm of an operator defined on a graph describing factorization, we will show how to bound that norm. In essence, the graph is a strong local expander, with all eigenvalues bounded by a constant factor times the theoretical minimum (i.e., the eigenvalue bound corresponding to Ramanujan graphs). The proof will take us on a walk from graph theory to linear algebra and the geometry of numbers, and back to graph theory, aided, along the way, by a generalized sieve. This is an expository paper; the full proof has appeared as a joint preprint with M. Radziwi\{l}\{l}.
