• 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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