On the Davenport-Heilbronn theorems and second order terms
Number Theory
2012-06-22 v3
Abstract
We give simple proofs of the Davenport--Heilbronn theorems, which provide the main terms in the asymptotics for the number of cubic fields having bounded discriminant and for the number of 3-torsion elements in the class groups of quadratic fields having bounded discriminant. We also establish second main terms for these theorems, thus proving a conjecture of Roberts. Our arguments provide natural interpretations for the various constants appearing in these theorems in terms of local masses of cubic rings.
Cite
@article{arxiv.1005.0672,
title = {On the Davenport-Heilbronn theorems and second order terms},
author = {Manjul Bhargava and Arul Shankar and Jacob Tsimerman},
journal= {arXiv preprint arXiv:1005.0672},
year = {2012}
}
Comments
38 pages