Independent relative units of low height
Shabnam Akhtari, Jeffery D. Vaaler
TL;DR
This paper establishes inequalities linking the relative regulator of a number field extension to the product of heights of its multiplicatively independent relative units, providing new insights into algebraic number theory.
Contribution
It introduces novel inequalities that connect the relative regulator with heights of units, advancing understanding of number field extensions.
Findings
Proved inequalities relating relative regulator and heights of units
Established bounds for multiplicatively independent relative units
Enhanced theoretical framework in algebraic number theory
Abstract
We prove inequalities that compare the relative regulator of an extension of number fields with a product of heights of multiplicatively independent relative units.
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Taxonomy
TopicsAnalytic Number Theory Research · Algebraic Geometry and Number Theory · Limits and Structures in Graph Theory