Norm-Euclidean Galois fields and the Generalized Riemann Hypothesis

2011/02/10 by McGown, Kevin J. · 1 citation
#11A05 #11R04 #11R16 (Primary) 11R80 #11Y40 (Secondary) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1102.2043

Abstract

Assuming the Generalized Riemann Hypothesis (GRH), we show that the norm-Euclidean Galois cubic fields are exactly those with discriminant Δ=7²,9²,13²,19²,31²,37²,43²,61²,67²,103²,109²,127²,157². A large part of the proof is in establishing the following more general result: Let K be a Galois number field of odd prime degree ℓ and conductor f. Assume the GRH for ζ_K(s). If 38(ℓ-1)²(log f)⁶loglog f

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