Error estimates for the Davenport-Heilbronn theorems

DOI10.1215/00127094-2010-007zbMath1227.11114OpenAlexW2049367305WikidataQ101094331 ScholiaQ101094331MaRDI QIDQ974799

Karim Belabas, Manjul Bhargava, Carl B. Pomerance

Publication date: 7 June 2010

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/00127094-2010-007

zbMATH Keywords

densityquadratic fielddiscriminantcubic fieldquartic field

Mathematics Subject Classification ID

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

Related Items

Omega results for cubic field counts via lower-order terms in the one-level density, Central limit theorem for Artin L-functions, Counting discriminants of number fields, On the average number of octahedral newforms of prime level, On the Davenport-Heilbronn theorems and second order terms, Moments of logarithmic derivatives of \(L\)-functions, Secondary terms in counting functions for cubic fields, On \(\ell\)-torsion in class groups of number fields, Statistics of genus numbers of cubic fields, Counting problems: class groups, primes, and number fields, The density of discriminants of $S_3$-sextic number fields, Arithmetic of octahedral sextics, Malle's conjecture for for, Levels of distribution for sieve problems in prehomogeneous vector spaces, SATO–TATE EQUIDISTRIBUTION OF CERTAIN FAMILIES OF ARTIN -FUNCTIONS, Low lying zeros of Artin \(L\)-functions, The number of ramified primes in number fields of small degree, COUNTING -FIELDS WITH A POWER SAVING ERROR TERM

Cites Work

• Cohen-Lenstra heuristic and roots of unity
• Higher composition laws. III: The parametrization of quartic rings
• Fourier coefficients of modular forms on \(G_2\).
• The density of discriminants of quartic rings and fields
• Counting discriminants of number fields
• Density of cubic field discriminants
• On the Computation of a Table of Complex Cubic Fields with Discriminant D > -10 6
• On Totally Real Cubic Fields
• The adelic zeta function associated to the space of binary cubic forms. II: Local theory.
• Density of discriminants of cubic extensions.
• On Totally Real Cubic Fields with Discriminant D < 10 7
• Heuristics on Class Groups: Some Good Primes are not too Good
• A fast algorithm to compute cubic fields
• Automorphic forms on GL(2) and the rank of class groups
• On quadratic fields with large 3-rank
• Orders of a quartic field
• Densities of quartic fields with even Galois groups
• On the density of discriminants of cubic fields. II
• On the Class-Number of Binary Cubic Forms (I)
• Algorithmic Number Theory
• Algorithmic Number Theory
• On Dirichlet series whose coefficients are class numbers of integral binary cubic forms
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