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In this chapter we define Artin’s L-functions and prove their functoriality properties. We further show that every L-function we encountered in the previous chapters is in fact an abelian L-function in the sense of Artin. Finally, assuming the results of Chapter 1, we prove that all Artin L-functions admit meromorphic continuation to the whole complex plane.

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The L-function of a Complex Galois Representation

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  • 发表日期：

    2025年

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  • Davide Lombardo

摘要

In this chapter we define Artin’s L-functions and prove their functoriality properties. We further show that every L-function we encountered in the previous chapters is in fact an abelian L-function in the sense of Artin. Finally, assuming the results of Chapter 1, we prove that all Artin L-functions admit meromorphic continuation to the whole complex plane.