On the Davenport-Heilbronn theorems and second order terms
Author(s): Bhargava, Manjul; Shankar, Arul; Tsimerman, Jacob
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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. |
Publication Date: | Aug-2013 |
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 |
DOI: | doi:10.1007/s00222-012-0433-0 |
ISSN: | 0020-9910 |
Pages: | 439 - 499 |
Type of Material: | Journal Article |
Journal/Proceeding Title: | INVENTIONES MATHEMATICAE |
Version: | Author's manuscript |
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