Reference : Explicit Kummer theory for the rational numbers
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/10993/39282
Explicit Kummer theory for the rational numbers
English
Perucca, Antonella mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Sgobba, Pietro mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Tronto, Sebastiano mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
2020
International Journal of Number Theory
World Scientific Publishing Co.
Yes (verified by ORBilu)
International
1793-0421
Singapore
[en] Number fields ; Kummer theory ; Degree ; Cyclotomic fields
[en] Let G be a finitely generated multiplicative subgroup of Q* having rank r. The ratio between n^r and the Kummer degree [Q(\zeta_m,\sqrt[n]{G}) : Q(\zeta_m)], where n divides m, is bounded independently of n and m. We prove that there exist integers m_0, n_0 such that the above ratio depends only on G, \gcd(m,m_0), and \gcd(n,n_0). Our results are very explicit and they yield an algorithm that provides formulas for all the above Kummer degrees (the formulas involve a finite case distinction).
Researchers
http://hdl.handle.net/10993/39282

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