Lower bounds for regulators of number fields in terms of their discriminants

Shabnam Akhtari; Jeffrey D. Vaaler

doi:10.5802/jtnb.1245

Lower bounds for regulators of number fields in terms of their discriminants

Shabnam Akhtari, Jeffrey D. Vaaler

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We prove inequalities that compare the regulator of a number field with the absolute value of its discriminant. We refine the ideas in Silver-man’s work [15] where such general inequalities are first proven. In order to prove our main theorems, we combine these refinements with the authors’ pre-vious results on bounding the product of heights of relative units in a number field extension.

Original language	English (US)
Pages (from-to)	259-282
Number of pages	24
Journal	Journal de Theorie des Nombres de Bordeaux
Volume	35
Issue number	1
DOIs	https://doi.org/10.5802/jtnb.1245
State	Published - 2023

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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10.5802/jtnb.1245

Cite this

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Lower bounds for regulators of number fields in terms of their discriminants

Abstract

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