Missing Class Groups and Class Number Statistics for Imaginary Quadratic Fields

DOI10.1080/10586458.2017.1383952zbMath1470.11285arXiv1510.04387OpenAlexW2963825179MaRDI QIDQ5382936

No author found.

Publication date: 19 June 2019

Published in: Experimental Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1510.04387

zbMATH Keywords

class groupsclass numbersCohen-Lenstra heuristics

Mathematics Subject Classification ID

Quadratic extensions (11R11) Algebraic number theory computations (11Y40) Class numbers, class groups, discriminants (11R29)

Related Items (7)

Nonholomorphic Ramanujan-type congruences for Hurwitz class numbers ⋮ The distribution of class numbers in a special family of real quadratic fields ⋮ On the distribution of Alexander polynomials in certain families of closed braids ⋮ The distribution of values of zeta and \(L\)-functions ⋮ Partitions associated to class groups of imaginary quadratic number fields ⋮ On the average of the number of imaginary quadratic fields with a given class number ⋮ The maximal discrete extension of the Hermitian modular group

Uses Software

• PARI/GP

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the Davenport-Heilbronn theorems and second order terms
• Secondary terms in counting functions for cubic fields
• On the average of the number of imaginary quadratic fields with a given class number
• The Cohen-Lenstra heuristic: methodology and results
• Quelques applications du théorème de densité de Chebotarev
• Construction of number fields with prescribed \(\ell\)-class groups
• On the ideal class group problem for global fields
• The distribution of values of \(L(1,\chi_d)\)
• The global Cohen-Lenstra heuristic
• Construction of maximal unramified \(p\)-extensions with prescribed Galois groups
• Every Abelian group is a class group
• On unramified Galois extensions of quadratic number fields
• Density of cubic field discriminants
• Unconditional class group tabulation of imaginary quadratic fields to $\|\Delta \| < 2^{40}$
• On Group Structures Realized by Elliptic Curves over Arbitrary Finite Fields
• A bound for the 3-part of class numbers of quadratic fields by means of the square sieve
• The number of imaginary quadratic fields with a given class number
• Imaginary quadratic fields with class group exponent 5
• Sharper Bounds for the Chebyshev Functions θ(x) and ψ(x). II
• A fast algorithm to compute cubic fields
• Class numbers of imaginary quadratic fields
• Conditional bounds for the least quadratic non-residue and related problems
• Probability Inequalities for Sums of Bounded Random Variables
• A Cohen-Lenstra phenomenon for elliptic curves
• Reflection Principles and Bounds for Class Group Torsion
• Automorphisms of Finite Abelian Groups
• Integral points on elliptic curves and 3-torsion in class groups
• Quadratic class numbers and character sums
• Exponents of the class groups of complex quadratic fields
• The Class Group of Dedekind Domains
• On the Exponent of the Ideal Class Groups of Complex Quadratic Fields
• Algorithmic Number Theory

This page was built for publication: Missing Class Groups and Class Number Statistics for Imaginary Quadratic Fields