论文标题
在射线课上计算理想
Counting ideals in ray classes
论文作者
论文摘要
令$ \ mathbf {k} $为一个数字字段，$ \ mathfrak {q} $是$ \ mathcal {o} _ {\ mathbf {k}} $中的积分理想。 Tatuzawa的结果是1973年的结果，计算缩小的$ \ Mathbf {k} $ modulo $ \ mathfrak {q} $的狭窄射线类组中最多$ x $的理想数量的渐近（带有错误术语）。此结果将错误项与一个常数界限，其对$ \ mathfrak {q} $的依赖性是明确的，但依赖于$ \ mathbf {k} $并不明确。本文的目的是证明这种渐近造成的，具有完全明确的误差术语。
Let $\mathbf{K}$ be a number field and $\mathfrak{q}$ an integral ideal in $\mathcal{O}_{\mathbf{K}}$. A result of Tatuzawa from 1973, computes the asymptotic (with an error term) for the number of ideals with norm at most $x$ in a class of the narrow ray class group of $\mathbf{K}$ modulo $\mathfrak{q}$. This result bounds the error term with a constant whose dependence on $\mathfrak{q}$ is explicit but dependence on $\mathbf{K}$ is not explicit. The aim of this paper is to prove this asymptotic with a fully explicit bound for the error term.
