L-series and homomorphisms of number fields

2019/10/27 by Harry Smit, Smit, Harry
Mathematics · #11R37 #11R42 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1910.12321

openalex publication_date 2019/10/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

While the zeta function does not determine a number field uniquely, the L-series of a well-chosen Dirichlet character does. Moreover, isomorphisms between two number fields are in natural bijection with L-series preserving isomorphisms of l-torsion subgroups of the Dirichlet character groups. We extend this by showing that homomorphisms between number fields are in natural bijection with group homomorphisms between l-torsion subgroups of the Dirichlet character groups abiding a divisibility condition on the L-series when l is sufficiently large.

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