论文标题
枚举$ d_4 $ Quartics和Galois集团偏向功能字段
Enumerating $D_4$ Quartics and a Galois Group Bias Over Function Fields
论文作者
论文摘要
我们给出了一个差异公式，该公式对于$ d_4 $ $ d_4 $四分之一的函数场的扩展，其判别性等于某些绑定，基本上重现了由于cohen，diaz y diaz和Olivier的数字字段的类似结果，但具有更强的误差项。我们还研究了功能字段的相对密度$ d_4 $和$ s_4 $四分之一的扩展，并表明在温和的条件下，$ d_4 $ d_4 $ QUYTENIC的数量远远超过了$ s_4 $ Quarticions的数量
We give an asymptotic formula for the number of $D_4$ quartic extensions of a function field with discriminant equal to some bound, essentially reproducing the analogous result over number fields due Cohen, Diaz y Diaz, and Olivier, but with a stronger error term. We also study the relative density of $D_4$ and $S_4$ quartic extensions of a function field and show that with mild conditions, the number of $D_4$ quartic extensions can far exceed the number of $S_4$ quartic extensions
