The shape of quartic fields
Number Theory
2018-01-12 v2
Abstract
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.
Cite
@article{arxiv.1706.09987,
title = {The shape of quartic fields},
author = {Robert Hough},
journal= {arXiv preprint arXiv:1706.09987},
year = {2018}
}
Comments
Added acknowledgement of financial support from NSF Grant DMS-1712682 "Probabilistic methods in discrete structures and applications."