Characterization of global fields by Dirichlet \(L\)-series

DOI10.1007/s40993-018-0143-9zbMath1460.11137arXiv1706.04515OpenAlexW2902736740MaRDI QIDQ2316322

Harry Smit, Xin Li, Bart de Smit, Matilde Marcolli, Gunther Cornelissen

Publication date: 26 July 2019

Published in: Research in Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1706.04515

zbMATH Keywords

class field theory\(L\)-seriesarithmetic equivalence

Mathematics Subject Classification ID

Coverings of curves, fundamental group (14H30) Class field theory (11R37) Zeta functions and (L)-functions of number fields (11R42) Adèle rings and groups (11R56)

Related Items (13)

Homotopic and geometric Galois theory. Abstracts from the workshop held March 7--13, 2021 (online meeting) ⋮ The \(m\)-step solvable anabelian geometry of number fields ⋮ Quantum statistical mechanics of the absolute Galois group ⋮ Stronger arithmetic equivalence ⋮ Two-step nilpotent extensions are not anabelian ⋮ Constructing number field isomorphisms from \(*\)-isomorphisms of certain crossed product \(\mathrm{C}^*\)-algebras ⋮ \(L\)-series and isomorphisms of number fields ⋮ Recovering algebraic curves from \(L\)-functions of Hilbert class fields ⋮ Pair arithmetical equivalence for quadratic fields ⋮ Reconstructing global fields from dynamics in the abelianized Galois group ⋮ Recovering affine curves over finite fields from \(L\)-functions ⋮ Additive structure of totally positive quadratic integers ⋮ The integral trace form as a complete invariant for real \(S_n\) number fields

Cites Work

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• Reconstructing global fields from dynamics in the abelianized Galois group
• Isomorphisms of Galois groups
• Isomorphisms of Galois groups of algebraic function fields
• Trivial \(L\)-functions for the rational function field
• On the field-theoreticity of homomorphisms between the multiplicative groups of number fields
• Endomorphisms of Abelian varieties over finite fields
• Kennzeichnung der p-adischen und der endlichen algebraischen Zahlkörper
• Quantum Statistical Mechanics, L-Series and Anabelian Geometry I: Partition Functions
• Imaginary quadratic fields with isomorphic abelian Galois groups
• Galois Group of the Maximal Abelian Extension over an Algebraic Number Field
• Field Arithmetic
• Curves, dynamical systems, and weighted point counting

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