A Multiquadratic Field Generalization of Artin's Conjecture

2012/02/15 by Maria Stadnik, Stadnik, Maria
Mathematics · #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #History and Theory of Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1202.3475

openalex publication_date 2012/02/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that (under the assumption of the generalized Riemann hypothesis) a totally real multiquadratic number field K has a positive density of primes p ∈ ℤ for which the image of the unit group (O_K)^×) in (O_K/pO_K)^×) has minimal index (p-1)/2 if and only if K contains a unit of norm -1.

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