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

1 Scopus citations

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

Access to Document

10.5802/jtnb.1245

Cite this

@article{8d43118be70347b6af6ea410e683e67f,

title = "Lower bounds for regulators of number fields in terms of their discriminants",

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{\textquoteright}s work [15] where such general inequalities are first proven. In order to prove our main theorems, we combine these refinements with the authors{\textquoteright} pre-vious results on bounding the product of heights of relative units in a number field extension.",

author = "Shabnam Akhtari and Vaaler, \{Jeffrey D.\}",

note = "Publisher Copyright: {\textcopyright} Les auteurs, 2023.",

year = "2023",

doi = "10.5802/jtnb.1245",

language = "English (US)",

volume = "35",

pages = "259--282",

journal = "Journal de Theorie des Nombres de Bordeaux",

issn = "1246-7405",

publisher = "Societe Arithmetique de Bordeaux",

number = "1",

}

TY - JOUR

T1 - Lower bounds for regulators of number fields in terms of their discriminants

AU - Akhtari, Shabnam

AU - Vaaler, Jeffrey D.

N1 - Publisher Copyright: © Les auteurs, 2023.

PY - 2023

Y1 - 2023

N2 - 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.

AB - 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.

UR - https://www.scopus.com/pages/publications/85159945879

UR - https://www.scopus.com/pages/publications/85159945879#tab=citedBy

U2 - 10.5802/jtnb.1245

DO - 10.5802/jtnb.1245

M3 - Article

AN - SCOPUS:85159945879

SN - 1246-7405

VL - 35

SP - 259

EP - 282

JO - Journal de Theorie des Nombres de Bordeaux

JF - Journal de Theorie des Nombres de Bordeaux

IS - 1

ER -

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

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this