Robert Hough
Published 2017-06-30Version 1
We use the method of Shintani, as developed by Taniguchi and Thorne, to prove the joint cuspidal equidistribution of the shape of quartic fields paired with the shape of its cubic resolvent, when the fields are ordered by discriminant. Our estimate saves a small power in the corresponding Weyl sums.
$\ell$-torsion in class groups of certain families of $D_4$-quartic fields
Diophantine problems related to cyclic cubic and quartic fields
An improved error term for $D_4$-quartic fields
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