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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
Version: Author's manuscript

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