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- W2937903557 abstract "For all number fields the failure of maximality for the Kummer extensions is bounded in a very strong sense. We give a direct proof (without relying on the Bashmakov–Ribet method) of the fact that if [Formula: see text] is a finitely generated and torsion-free multiplicative subgroup of a number field [Formula: see text] having rank [Formula: see text], then the ratio between [Formula: see text] and the Kummer degree [Formula: see text] is bounded independently of [Formula: see text]. We then apply this result to generalize to higher rank a theorem of Ziegler from 2006 about the multiplicative order of the reductions of algebraic integers (the multiplicative order must be in a given arithmetic progression, and an additional Frobenius condition may be considered)." @default.
- W2937903557 created "2019-04-25" @default.
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- W2937903557 date "2019-08-19" @default.
- W2937903557 modified "2023-09-23" @default.
- W2937903557 title "Kummer theory for number fields and the reductions of algebraic numbers" @default.
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- W2937903557 doi "https://doi.org/10.1142/s179304211950091x" @default.
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