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Addendum to: Reductions of algebraic integers [J. Number Theory 167 (2016) 259–283].
- Source :
-
Journal of Number Theory . Apr2020, Vol. 209, p391-395. 5p. - Publication Year :
- 2020
-
Abstract
- Let K be a number field, and let G be a finitely generated and torsion-free subgroup of K ×. We consider Kummer extensions of G of the form K (ζ 2 m , G 2 n ) / K (ζ 2 m ) , where n ⩽ m. In the paper by Debry and Perucca (2016) [1] , the degrees of those extensions have been evaluated in terms of divisibility parameters over K (ζ 4). We prove how properties of G over K explicitly determine the divisibility parameters over K (ζ 4). This result yields a clear computational advantage, since no field extension is required. [ABSTRACT FROM AUTHOR]
- Subjects :
- *NUMBER theory
*DIVISIBILITY groups
*INTEGERS
*CYCLOTOMIC fields
Subjects
Details
- Language :
- English
- ISSN :
- 0022314X
- Volume :
- 209
- Database :
- Academic Search Index
- Journal :
- Journal of Number Theory
- Publication Type :
- Academic Journal
- Accession number :
- 140987779
- Full Text :
- https://doi.org/10.1016/j.jnt.2019.09.004