Geodesic
A generalization of Dirichlet's unit theorem
Paul Fili 1   ; Zachary Miner 2
1 Department of Mathematics University of Rochester Rochester, NY 14627, U.S.A.
2 Department of Mathematics University of Texas at Austin Austin, TX 78712, U.S.A.
Acta Arithmetica, Tome 162 (2014) no. 4, pp. 355-368 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

Voir la notice de l'article

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 $\mathbb {Q}$-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 $\mathbb {Q}$ retain their linear independence over $\mathbb {R}$.
DOI : 10.4064/aa162-4-3
Keywords: generalize dirichlets s unit theorem usual group s units number field infinite rank group algebraic numbers having nontrivial valuations only places lying specifically demonstrate group algebraic s units modulo torsion mathbb vector space which normed weil height spans hyperplane determined product formula elements vector space which linearly independent mathbb retain their linear independence mathbb

Paul Fili  1   ; Zachary Miner  2

1 Department of Mathematics University of Rochester Rochester, NY 14627, U.S.A.
2 Department of Mathematics University of Texas at Austin Austin, TX 78712, U.S.A. 
@article{10_4064_aa162_4_3,
     author = {Paul Fili and Zachary Miner},
     title = {A generalization of {Dirichlet's} unit theorem},
     journal = {Acta Arithmetica},
     pages = {355--368},
     year = {2014},
     volume = {162},
     number = {4},
     doi = {10.4064/aa162-4-3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/aa162-4-3/}
}
TY  - JOUR
AU  - Paul Fili
AU  - Zachary Miner
TI  - A generalization of Dirichlet's unit theorem
JO  - Acta Arithmetica
PY  - 2014
SP  - 355
EP  - 368
VL  - 162
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4064/aa162-4-3/
DO  - 10.4064/aa162-4-3
LA  - en
ID  - 10_4064_aa162_4_3
ER  - 
%0 Journal Article
%A Paul Fili
%A Zachary Miner
%T A generalization of Dirichlet's unit theorem
%J Acta Arithmetica
%D 2014
%P 355-368
%V 162
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4064/aa162-4-3/
%R 10.4064/aa162-4-3
%G en
%F 10_4064_aa162_4_3
Paul Fili; Zachary Miner. A generalization of Dirichlet's unit theorem. Acta Arithmetica, Tome 162 (2014) no. 4, pp. 355-368. doi: 10.4064/aa162-4-3

Cité par Sources :