Are number fields determined by Artin L-Functions ?

Juergen Klueners; Florin Nicolae

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arXiv · 1509.06883

Are number fields determined by Artin L-Functions ?

Juergen Klueners·Florin Nicolae

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Abstract

Let $k$ be a number field, $K/k$ a finite Galois extension with Galois group $G$, $\chi$ a faithful character of $G$. We prove that the Artin L-function $L(s,\chi,K/k)$ determines the Galois closure of $K$ over $\Q$. In the special case $k=\Q$ it also determines the character $\chi$.

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Juergen Klueners, Florin Nicolae. 2015-09-23. Are number fields determined by Artin L-Functions ?. https://arxiv.org/abs/1509.06883

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