Quantum Statistical Mechanics, L-Series and Anabelian Geometry I: Partition Functions

DOI10.1007/978-3-319-05254-0_4zbMath1329.82007arXiv1009.0736OpenAlexW1593258072MaRDI QIDQ2948973

Gunther Cornelissen, Matilde Marcolli

Publication date: 7 October 2015

Published in: Trends in Contemporary Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1009.0736

zbMATH Keywords

Galois groupzeta functionabelian class field theoryquantum statistical mechanical system

Mathematics Subject Classification ID

Galois theory (11R32) (zeta (s)) and (L(s, chi)) (11M06) Applications of selfadjoint operator algebras to physics (46L60) Quantum equilibrium statistical mechanics (general) (82B10) Class field theory (11R37) Modular and Shimura varieties (14G35)

Related Items (16)

Endomotives of toric varieties ⋮ Irreducible representations of Bost-Connes systems ⋮ Bost-Connes systems, Hecke algebras, and induction ⋮ Partition functions as \(C^*\)-dynamical invariants and actions of congruence monoids ⋮ Hecke algebra isomorphisms and adelic points on algebraic groups ⋮ Graph reconstruction and quantum statistical mechanics ⋮ Quantum Statistical Mechanics, L-Series and Anabelian Geometry I: Partition Functions ⋮ On \(K\)-theoretic invariants of semigroup \(C^*\)-algebras attached to number fields ⋮ Constructing number field isomorphisms from \(*\)-isomorphisms of certain crossed product \(\mathrm{C}^*\)-algebras ⋮ Isomorphism invariants for multivariable \(C^\ast\)-dynamics ⋮ Reconstructing global fields from dynamics in the abelianized Galois group ⋮ Quantum statistical mechanics in arithmetic topology ⋮ The spectral length of a map between Riemannian manifolds ⋮ Semicrossed products of operator algebras by semigroups ⋮ Twisted spectral triples and quantum statistical mechanical systems ⋮ Characterization of global fields by Dirichlet \(L\)-series

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• Quantum Statistical Mechanics, L-Series and Anabelian Geometry I: Partition Functions
• On the adele rings of algebraic number fields
• Zeta functions do not determine class numbers
• Curves, dynamical systems, and weighted point counting

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