A Secondary Term for $D_4$ Quartic Fields Ordered By Conductor

Published 7 Nov 2021 in math.NT | (2111.03982v1)

Abstract: To any quartic $D_4$ extension of $\mathbb{Q}$, one can associate the Artin conductor of a 2-dimensional irreducible representation of the group. Alt\u{u}g, Shankar, Varma, and Wilson determined the asymptotic number of such fields when ordered by conductor. We refine this, realizing a secondary term and power saving error term.

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Authors (1)

Matthew Friedrichsen

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