A generalization of Dirichlet's unit theorem

Paul Fili, and Zachary Miner. "A generalization of Dirichlet's unit theorem." Acta Arithmetica 162.4 (2014): 355-368. <http://eudml.org/doc/279334>.

@article{PaulFili2014,
abstract = {We generalize Dirichlet's S-unit theorem from the usual group of S-units of a number field K to the infinite rank group of all algebraic numbers having nontrivial valuations only on places lying over S. Specifically, we demonstrate that the group of algebraic S-units modulo torsion is a ℚ-vector space which, when normed by the Weil height, spans a hyperplane determined by the product formula, and that the elements of this vector space which are linearly independent over ℚ retain their linear independence over ℝ.},
author = {Paul Fili, Zachary Miner},
journal = {Acta Arithmetica},
keywords = {Dirichlet's unit theorem; algebraic numbers; Weil height},
language = {eng},
number = {4},
pages = {355-368},
title = {A generalization of Dirichlet's unit theorem},
url = {http://eudml.org/doc/279334},
volume = {162},
year = {2014},
}

TY - JOUR
AU - Paul Fili
AU - Zachary Miner
TI - A generalization of Dirichlet's unit theorem
JO - Acta Arithmetica
PY - 2014
VL - 162
IS - 4
SP - 355
EP - 368
AB - We generalize Dirichlet's S-unit theorem from the usual group of S-units of a number field K to the infinite rank group of all algebraic numbers having nontrivial valuations only on places lying over S. Specifically, we demonstrate that the group of algebraic S-units modulo torsion is a ℚ-vector space which, when normed by the Weil height, spans a hyperplane determined by the product formula, and that the elements of this vector space which are linearly independent over ℚ retain their linear independence over ℝ.
LA - eng
KW - Dirichlet's unit theorem; algebraic numbers; Weil height
UR - http://eudml.org/doc/279334
ER -