Lower order terms in the shape of cubic fields
Number Theory
2024-09-16 v1
Abstract
We demonstrate equidistribution of the lattice shape of cubic fields when ordered by discriminant, giving an estimate in the Eisenstein series spectrum with a lower order main term. The analysis gives a separate discussion of the contributions of reducible and irreducible binary cubic forms, following a method of Shintani. Our work answers a question posed at the American Institute of Math by giving a precise geometric and spectral description of an evident barrier to equidistribution in the lattice shape.
Cite
@article{arxiv.2409.08417,
title = {Lower order terms in the shape of cubic fields},
author = {Robert Hough and Eun Hye Lee},
journal= {arXiv preprint arXiv:2409.08417},
year = {2024}
}
Comments
Preliminary version. arXiv admin note: substantial text overlap with arXiv:2007.03170