论文标题
计数问题：课程组，素数和数字字段
Counting problems: class groups, primes, and number fields
论文作者
论文摘要
每个数字字段都有一个相关的有限阿贝尔组，该组类别组，该组记录了算术在该字段整数中的某些属性。班级团体经过深入研究，但仍然神秘。 Brumer和Silverman的中心猜想指出，对于每个Prime $ \ ell $，每个数字字段的属性都有其类组的属性，几乎没有订单$ \ ell $的元素，其中“很少”与该字段的绝对歧视相对于“很少”。本文调查了该猜想的最新进展，并概述了其与计数质数，计数固定判别的数字字段的密切联系，并计算有界判别的数字字段。
Each number field has an associated finite abelian group, the class group, that records certain properties of arithmetic within the ring of integers of the field. The class group is well-studied, yet also still mysterious. A central conjecture of Brumer and Silverman states that for each prime $\ell$, every number field has the property that its class group has very few elements of order $\ell$, where "very few" is measured relative to the absolute discriminant of the field. This paper surveys recent progress toward this conjecture, and outlines its close connections to counting prime numbers, counting number fields of fixed discriminant, and counting number fields of bounded discriminant.
