Explicit Form of Cassels’ p-adic Embedding Theorem for Number Fields
Canadian journal of mathematics, Tome 67 (2015) no. 5, pp. 1046-1064
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In this paper, we give a general explicit form of Cassels’ $p$ -adic embedding theorem for number fields. We also give its refined form in the case of cyclotomic fields. As a byproduct, given an irreducible polynomial $f$ over $\mathbb{Z}$ , we give a general unconditional upper bound for the smallest prime number $p$ such that $f$ has a simple root modulo $p$ .
Mots-clés :
11R04, 11S85, 11G50, 11R09, 11R18, number field, p-adic embedding, height, polynomial, cyclotomic field
Dubickas, Arturas; Sha, Min; Shparlinski, Igor. Explicit Form of Cassels’ p-adic Embedding Theorem for Number Fields. Canadian journal of mathematics, Tome 67 (2015) no. 5, pp. 1046-1064. doi: 10.4153/CJM-2015-021-2
@article{10_4153_CJM_2015_021_2,
author = {Dubickas, Arturas and Sha, Min and Shparlinski, Igor},
title = {Explicit {Form} of {Cassels{\textquoteright}} p-adic {Embedding} {Theorem} for {Number} {Fields}},
journal = {Canadian journal of mathematics},
pages = {1046--1064},
year = {2015},
volume = {67},
number = {5},
doi = {10.4153/CJM-2015-021-2},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2015-021-2/}
}
TY - JOUR AU - Dubickas, Arturas AU - Sha, Min AU - Shparlinski, Igor TI - Explicit Form of Cassels’ p-adic Embedding Theorem for Number Fields JO - Canadian journal of mathematics PY - 2015 SP - 1046 EP - 1064 VL - 67 IS - 5 UR - http://geodesic.mathdoc.fr/articles/10.4153/CJM-2015-021-2/ DO - 10.4153/CJM-2015-021-2 ID - 10_4153_CJM_2015_021_2 ER -
%0 Journal Article %A Dubickas, Arturas %A Sha, Min %A Shparlinski, Igor %T Explicit Form of Cassels’ p-adic Embedding Theorem for Number Fields %J Canadian journal of mathematics %D 2015 %P 1046-1064 %V 67 %N 5 %U http://geodesic.mathdoc.fr/articles/10.4153/CJM-2015-021-2/ %R 10.4153/CJM-2015-021-2 %F 10_4153_CJM_2015_021_2
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