On the Computation of the Class Number of an Algebraic Number Field

DOI10.2307/2008730zbMath0677.12003OpenAlexW4236385849MaRDI QIDQ3832668

Johannes A. Buchmann, Hugh C. Williams

Publication date: 1989

Full work available at URL: https://doi.org/10.2307/2008730

zbMATH Keywords

generalized Riemann hypothesisregulatorEuler factorsalgorithm for computing the class number

Mathematics Subject Classification ID

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

Related Items (4)

Algorithms in Algebraic Number Theory ⋮ Approximating Euler products and class number computation in algebraic function fields ⋮ Explicit bounds for residues of Dedekind zeta functions, values of \(L\)-functions at \(s=1\), and relative class numbers ⋮ The exponent three class group problem for some real cyclic cubic number fields

Cites Work

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• Explicit methods in number theory. Abstracts from the workshop held July 15--21, 2007.
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• Computation of class numbers by an analytic method
• The construction of maximal orders over a Dedekind domain
• On the computation of units and class numbers by a generalization of Lagrange's algorithm
• Improved Methods for Calculating Vectors of Short Length in a Lattice, Including a Complexity Analysis
• A Note on Class-Number One in Certain Real Quadratic and Pure Cubic Fields
• On Effective Computation of Fundamental Units. I
• A Computational Technique for Evaluating L(1, χ) and the Class Number of a Real Quadratic Field
• A Factorization of the Densities of the Ideals in Algebraic Number Fields

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