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Artin L Functions

  • Ehud de Shalit

Abstract

Let χ : (ℤ/mℤ)× → ℂ× be a primitive Dirichlet character modulo m. Let K = ℚ(ζ), where ζ = e 2πi/m . The identification G = Gal(K/ℚ) ≃ (ℤ/mℤ)× allows us to attach to χ a character χ Gal : G → ℂ× satisfying 1.1 if (p, m) = 1 and σ p is the Frobenius automorphism at p (the canonical generator of the decomposition group of p in G, which induces on the residue field of any prime of K above p the automorphism xx p .) The Kronecker-Weber theorem (Kronecker 1853, Weber 1886) asserts that every 1-dimensional character of G = Gal(̄ℚ/ℚ) is of the form χ Gal for an appropriate χ.

Keywords

Modular Form Riemann Hypothesis Class Field Theory Meromorphic Continuation Archimedean Place 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 2004

Authors and Affiliations

  • Ehud de Shalit

There are no affiliations available

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