论文标题
$ d_4 $ - Quartic Extensions of Indictant订购的数字字段的$ D_4 $ Quartic Extensions数量的电力错误项
Power-saving error terms for the number of $D_4$-quartic extensions over a number field ordered by discriminant
论文作者
论文摘要
我们研究了具有相对判别性界限的固定数字场上二面四分之一扩展的渐近计数。该计数的主要术语（包括在文献中找到的总结公式）（请参见Cohen--diaz y Diaz-无需证明的声明，请参见klüners以提供证明），但是尚未明确确定错误术语的节省功率，除非基本场是$ \ nathbb $ \ nathbb basbb。在本文中，我们描述了获得明确的主术语和省电误差术语的论点，该术语的$ d_4 $ Quartic Extensions是根据其相对判别物的规范排序的一般基本数字字段。我们还对数字渐近学的历史和发展进行了广泛的概述。
We study the asymptotic count of dihedral quartic extensions over a fixed number field with bounded norm of the relative discriminant. The main term of this count (including a summation formula for the constant) can be found in the literature (see Cohen--Diaz y Diaz--Olivier for the statement without proof and see Klüners for a proof), but a power-saving for the error term has not been explicitly determined except in the case that the base field is $\mathbb{Q}$. In this article, we describe the argument for obtaining both the explicit main term and a power-saving error term for the number of $D_4$-quartic extensions over a general base number field ordered by the norms of their relative discriminants. We also give an extensive overview of the history and development of number field asymptotics.
