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|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 con- stants appearing in these theorems in terms of local masses of cubic rings.|
|Electronic Publication Date:||11-Dec-2012|
|Citation:||Bhargava, Manjul, Shankar, Arul, Tsimerman, Jacob. (2013). On the Davenport-Heilbronn theorems and second order terms. INVENTIONES MATHEMATICAE, 193 (439 - 499. doi:10.1007/s00222-012-0433-0|
|Pages:||439 - 499|
|Type of Material:||Journal Article|
|Journal/Proceeding Title:||INVENTIONES MATHEMATICAE|
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