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Bibliographic Details
Main Authors: Shankar, Arul, Tsimerman, Jacob
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2503.02381
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Table of Contents:
  • We prove that the smoothed counting function of the set of quartic fields, satisfying any finite set of local conditions, can be written as a linear combination of $X,X^{5/6}\log X,X^{5/6}$, upto an error term of $O(X^{13/16+o(1)})$. For certain sets of local conditions, namely, those cutting out ``$S_4$-families'' of quartic fields, we explicitly determine the leading constants of the secondary terms. We moreover express these constants in terms of secondary mass formulas associated to families of quartic fields