On the Davenport-Heilbronn theorems and second order terms

DOI10.1007/s00222-012-0433-0zbMath1294.11191arXiv1005.0672OpenAlexW2151787442WikidataQ115396278 ScholiaQ115396278MaRDI QIDQ368620

Manjul Bhargava, Arul Shankar, Jacob Tsimerman

Publication date: 23 September 2013

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1005.0672

zbMATH Keywords

asymptotic methodsdiscriminantShintani zeta functioncubic extension\(3\)-class groupbinary cubic formpre-homogeneous vector space

Mathematics Subject Classification ID

Quadratic extensions (11R11) Cubic and quartic extensions (11R16) Class numbers, class groups, discriminants (11R29) Density theorems (11R45)

Related Items (44)

On Malle’s conjecture for nilpotent groups ⋮ Subconvexity of Shintani’s zeta function ⋮ Numerical secondary terms in a Cohen-Lenstra conjecture on real quadratic fields ⋮ Omega results for cubic field counts via lower-order terms in the one-level density ⋮ Number fields with prescribed norms (with an appendix by Yonatan Harpaz and Olivier Wittenberg) ⋮ ORBIT PARAMETRIZATIONS FOR K3 SURFACES ⋮ On class groups of imaginary quadratic fields ⋮ The mean values of cubic \(L\)-functions over function fields ⋮ Explicit methods for the Hasse norm principle and applications toA_nandS_nextensions ⋮ Averages and higher moments for the \(\ell\)-torsion in class groups ⋮ Construction of all cubic function fields of a given square-free discriminant ⋮ Secondary terms in counting functions for cubic fields ⋮ On \(\ell\)-torsion in class groups of number fields ⋮ ON THE -RANK OF CLASS GROUPS OF DIRICHLET BIQUADRATIC FIELDS ⋮ Zeta Functions for the Adjoint Action of GL(n) and Density of Residues of Dedekind Zeta Functions ⋮ The average size of the 3‐isogeny Selmer groups of elliptic curves y2=x3+k ⋮ Statistics of genus numbers of cubic fields ⋮ Counting problems: class groups, primes, and number fields ⋮ The density of discriminants of quintic rings and fields ⋮ A positive proportion of quartic fields are not monogenic yet have no local obstruction to being so ⋮ The value-distribution of Artin \(L\)-functions associated with cubic fields in conductor aspect ⋮ Heuristics for the asymptotics of the number of Sn$S_n$‐number fields ⋮ The mean number of 3-torsion elements in ray class groups of quadratic fields ⋮ Averages and moments associated to class numbers of imaginary quadratic fields ⋮ Missing Class Groups and Class Number Statistics for Imaginary Quadratic Fields ⋮ Nonabelian Cohen-Lenstra moments ⋮ Shintani’s zeta function is not a finite sum of Euler products ⋮ Modeling λ‐invariants by p‐adic random matrices ⋮ The mean number of 3-torsion elements in the class groups and ideal groups of quadratic orders ⋮ Self-dual Artin representations of dimension three ⋮ Dirichlet series associated to cubic fields with given quadratic resolvent ⋮ Equidistribution of shapes of complex cubic fields of fixed quadratic resolvent ⋮ Class field theory, Diophantine analysis and the asymptotic Fermat's last theorem ⋮ Malle's conjecture for for ⋮ Binary quartic forms with bounded invariants and small Galois groups ⋮ Levels of distribution for sieve problems in prehomogeneous vector spaces ⋮ SATO–TATE EQUIDISTRIBUTION OF CERTAIN FAMILIES OF ARTIN -FUNCTIONS ⋮ Cohen-Lenstra heuristics and local conditions ⋮ The shape of cubic fields ⋮ Large families of elliptic curves ordered by conductor ⋮ Statistics of \(K\)-groups modulo \(p\) for the ring of integers of a varying quadratic number field ⋮ Equidistribution of bounded torsion CM points ⋮ The number of ramified primes in number fields of small degree ⋮ Invariants for A₄ fields and the Cohen–Lenstra heuristics

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