Class numbers of real cyclotomic fields of prime conductor

DOI10.1090/S0025-5718-02-01432-1zbMath1052.11071OpenAlexW2019228100MaRDI QIDQ4794650

René Schoof

Publication date: 19 February 2003

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0025-5718-02-01432-1

Mathematics Subject Classification ID

Algebraic number theory computations (11Y40) Class numbers, class groups, discriminants (11R29) Cyclotomic extensions (11R18)

Related Items (24)

Invariant generalized ideal classes -- structure theorems for \(p\)-class groups in \(p\)-extensions ⋮ Class numbers of ray class fields of imaginary quadratic fields ⋮ On the class numbers of real cyclotomic fields of conductor pq ⋮ Greenberg’s conjecture for real quadratic fields and the cyclotomic ℤ₂-extensions ⋮ “Lights Out” and Variants ⋮ New criteria for Vandiver's conjecture using Gauss sums -- heuristics and numerical experiments ⋮ Log-\(\mathcal{S}\)-unit lattices using explicit Stickelberger generators to solve approx ideal-SVP ⋮ Primes of higher degree and annihilators of class groups ⋮ A NOTE ON THE EQUIVALENCE OF THE PARITY OF CLASS NUMBERS AND THE SIGNATURE RANKS OF UNITS IN CYCLOTOMIC FIELDS ⋮ The special case of cyclotomic fields in quantum algorithms for unit groups ⋮ Units in real cyclic fields ⋮ Power integral bases in prime-power cyclotomic fields ⋮ On the history of the study of ideal class groups ⋮ Class numbers in cyclotomic \(\mathbb{Z}_p\)-extensions ⋮ Short Stickelberger Class Relations and Application to Ideal-SVP ⋮ An application of the -adic analytic class number formula ⋮ Visibility of ideal classes ⋮ On the computation of class numbers of real abelian fields ⋮ Infinite families of cyclotomic function fields with any prescribed class group rank ⋮ Class groups of real cyclotomic fields ⋮ Genus theory and \(\varepsilon\)-conjectures on \(p\)-class groups ⋮ Real cyclotomic fields of prime conductor and their class numbers ⋮ On the units generated by Weierstrass forms ⋮ Class numbers of real cyclotomic fields of composite conductor

Uses Software

• PARI/GP

Cites Work

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• The determination of units in real cyclic sextic fields
• Anderson's module for cyclotomic fields of prime conductor
• Units of a family of fields related to the curve \(X_ 1(25)\).
• Jacobi sums and new families of irreducible polynomials of Gaussian periods
• Note on a Polynomial of Emma Lehmer
• Quintic Polynomials and Real Cyclotomic Fields with Large Class Number
• The Simplest Cubic Fields
• Méthodes et algorithmes pour le calcul numérique du nombre de classes et de unités des extensions cubiques cycliques de Q.
• Minus class groups of the fields of the 𝑙-th roots of unity
• Special Units in Real Cyclic Sextic Fields
• Class Number Computations of Real Abelian Number Fields

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