Two number fields with equal Dedekind zeta function are not necessarily isomorphic. However, if the number fields have equal sets of Dirichlet $L$-series then they \emph{are} isomorphic. We extend this result by showing that the isomorphisms between the number fields are in bijection with $L$-series preserving isomorphisms between the character groups.

中文翻译：

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数域的 L 级数和同构

具有相等 Dedekind zeta 函数的两个数域不一定是同构的。但是，如果数字字段具有相等的狄利克雷 $L$ 系列集合，则它们 \emph{are} 同构。我们通过显示数字字段之间的同构与 $L$-series 保持字符组之间的同构双射来扩展这个结果。