• Corpus ID: 119134240

A Note on Number Fields Sharing the List of Dedekind Zeta-Functions of Abelian Extensions with some Applications towards the Neukirch-Uchida Theorem

@article{Solomatin2019ANO,
  title={A Note on Number Fields Sharing the List of Dedekind Zeta-Functions of Abelian Extensions with some Applications towards the Neukirch-Uchida Theorem},
  author={Pavel Solomatin},
  journal={arXiv: Number Theory},
  year={2019}
}
  • P. Solomatin
  • Published 26 January 2019
  • Mathematics
  • arXiv: Number Theory
Given a number field $K$ one associates to it the set $\Lambda_K$ of Dedekind zeta-functions of finite abelian extensions of $K$. In this short note we present a proof of the following Theorem: for any number field $K$ the set $\Lambda_K$ determines the isomorphism class of $K$. This means that if for any number field $K'$ the two sets $\Lambda_K$ and $\Lambda_{K'}$ coincide, then $K \simeq K'$. As a consequence of this fact we deduce an alternative approach towards the proof of Neukirch-Uchida… 
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References

SHOWING 1-5 OF 5 REFERENCES
On Artin L-functions and Gassmann Equivalence for Global Function Fields
In this paper we present an approach to study arithmetical properties of global function fields by working with Artin L-functions. In particular we recall and then extend a criteria of two function…
Reconstructing global fields from Dirichlet L-series
We prove that two global fields are isomorphic if and only if there is an isomorphism of groups of Dirichlet characters that preserves L-series.
COHOMOLOGY OF NUMBER FIELDS (Grundlehren der Mathematischen Wissenschaften 323) By J ÜRGEN N EUKIRCH , A LEXANDER S CHMIDT and K AY W INGBERG 699 pp., £61.50, ISBN 3-540-66671-0 (Springer, Berlin, 2000).
Isomorphisms of Galois groups
Kennzeichnung der endlich-algebraischen Zahlkörper durch die Galoisgruppe der maximal auflösbaren Erweiterungen.