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arXiv · 2009.09274

Enumerating $D_4$ Quartics and a Galois Group Bias Over Function Fields

Daniel Keliher
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Abstract

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

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Daniel Keliher. 2020-09-19. Enumerating $D_4$ Quartics and a Galois Group Bias Over Function Fields. https://arxiv.org/abs/2009.09274

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