Zeta functions do not determine class numbers

DOI10.1090/S0273-0979-1994-00520-8zbMath0814.11053arXivmath/9410216OpenAlexW2014793770MaRDI QIDQ4310800

Bart de Smit, Robert Perlis

Publication date: 3 November 1994

Published in: Bulletin of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/9410216

zbMATH Keywords

zeta functionsarithmetically equivalent fieldsdifferent class numbersfields with isomorphic adele rings

Mathematics Subject Classification ID

Class numbers, class groups, discriminants (11R29) Zeta functions and (L)-functions of number fields (11R42)

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Tables of octic fields with a quartic subfield ⋮ On \(K\)-theoretic invariants of semigroup \(C^\ast\)-algebras attached to number field. II ⋮ Irreducible representations of Bost-Connes systems ⋮ Quantum Statistical Mechanics, L-Series and Anabelian Geometry I: Partition Functions ⋮ On \(K\)-theoretic invariants of semigroup \(C^*\)-algebras attached to number fields ⋮ Locally equivalent correspondences ⋮ Stronger arithmetic equivalence ⋮ Arithmetically equivalent number fields have approximately the same successive minima ⋮ On arithmetically equivalent fields with distinct \(p\)-class numbers. ⋮ A refined notion of arithmetically equivalent number fields, and curves with isomorphic Jacobians ⋮ Arithmetic equivalence for non-geometric extensions of global function fields ⋮ Semigroup C∗-Algebras

Cites Work

• Unnamed Item
• Analytic formulas for the regulator of a number field
• On the equation \(\zeta_K(s)=\zeta_{K'}(s)\)
• On the class numbers of arithmetically equivalent fields