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Faithful Artin induction and the Chebotarev density theorem

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arxiv 2405.08383 v1 pith:MGDAK4OU submitted 2024-05-14 math.NT math.GR

Robert J. Lemke Oliver , Alexander Smith This is my paper · ORCID
classification math.NTmath.GR
keywords chebotarevdensitytheoremcharactersfaithfulnumberspacevector
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Given a finite group G, we prove that the vector space spanned by the faithful irreducible characters of G is generated by the monomial characters in the vector space. As a consequence, we show that in any family of G-extensions of a fixed number field F, almost all are subject to a strong effective version of the Chebotarev density theorem. We use this version of the Chebotarev density theorem to deduce several consequences for class groups in families of number fields.

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  1. Inductive methods for counting number fields

    math.NT 2025-01 conditional novelty 8.0 of 10

    Introduces a fiber-summation inductive method that proves new cases of Malle's conjecture and gives counterexamples to Malle's predicted exponents for wreath products.

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