Lower Bounds for Regulators of Number Fields in terms of their Discriminants

2021/12/31 by Shabnam Akhtari, Akhtari, Shabnam, Jeffrey D. Vaaler +1 · 1 citation
Mathematics · #Analytic Number Theory Research #FOS: Mathematics #Limits and Structures in Graph Theory #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2112.15268

openalex publication_date 2021/12/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove inequalities that compare the regulator of a number field with its absolute discriminant. We refine some ideas in Silverman's work in 1984 where such general inequalities are first proven. In order to prove our main theorems, we combine these refinements with the authors' recent results on bounding the product of heights of relative units in a number field extension.

Cited by

• Unit lattices of D₄-quartic number fields with signature (2,1)

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