On trace-one generators of abelian cubic fields

2024/07/14 by O'Desky, Andrew
#11C08 #11G50 #14M25 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2407.10343

Abstract

Let K be a tamely ramified abelian cubic number field with discriminant D_K. We prove that the number of trace-one monic integral polynomials with root field K and height H is equal to the number of ideals in the quadratic field \mathbb Q(√(-3)) with norm H² D_K^-1/2.

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