# A generalization of Dirichlet's unit theorem

Acta Arithmetica (2014)

- Volume: 162, Issue: 4, page 355-368
- ISSN: 0065-1036

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topPaul 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 -

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