Heights, regulators and Schinzel's determinant inequality

Shabnam Akhtari, and Jeffrey D. Vaaler. "Heights, regulators and Schinzel's determinant inequality." Acta Arithmetica 172.3 (2016): 285-298. <http://eudml.org/doc/278887>.

@article{ShabnamAkhtari2016,
abstract = {We prove inequalities that compare the size of an S-regulator with a product of heights of multiplicatively independent S-units. Our upper bound for the S-regulator follows from a general upper bound for the determinant of a real matrix proved by Schinzel. The lower bound for the S-regulator follows from Minkowski's theorem on successive minima and a volume formula proved by Meyer and Pajor. We establish similar upper bounds for the relative regulator of an extension l/k of number fields.},
author = {Shabnam Akhtari, Jeffrey D. Vaaler},
journal = {Acta Arithmetica},
keywords = {S-regulator; Weil height},
language = {eng},
number = {3},
pages = {285-298},
title = {Heights, regulators and Schinzel's determinant inequality},
url = {http://eudml.org/doc/278887},
volume = {172},
year = {2016},
}

TY - JOUR
AU - Shabnam Akhtari
AU - Jeffrey D. Vaaler
TI - Heights, regulators and Schinzel's determinant inequality
JO - Acta Arithmetica
PY - 2016
VL - 172
IS - 3
SP - 285
EP - 298
AB - We prove inequalities that compare the size of an S-regulator with a product of heights of multiplicatively independent S-units. Our upper bound for the S-regulator follows from a general upper bound for the determinant of a real matrix proved by Schinzel. The lower bound for the S-regulator follows from Minkowski's theorem on successive minima and a volume formula proved by Meyer and Pajor. We establish similar upper bounds for the relative regulator of an extension l/k of number fields.
LA - eng
KW - S-regulator; Weil height
UR - http://eudml.org/doc/278887
ER -