Kummer theory for number fields and the reductions of algebraic numbers

DOI10.1142/S179304211950091XzbMath1451.11123OpenAlexW2937903557WikidataQ114071962 ScholiaQ114071962MaRDI QIDQ5232173

Antonella Perucca, Pietro Sgobba

Publication date: 30 August 2019

Published in: International Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s179304211950091x

zbMATH Keywords

reductiondensityKummer theorymultiplicative ordernumber field

Mathematics Subject Classification ID

Other number fields (11R21) Applications of sieve methods (11N36) Distribution of prime ideals (11R44) Cyclotomic extensions (11R18)

Related Items (9)

EXPLICIT KUMMER THEORY FOR QUADRATIC FIELDS ⋮ On the distribution of the order and index for the reductions of algebraic numbers ⋮ Simultaneous insolvability of exponential congruences ⋮ Divisibility conditions on the order of the reductions of algebraic numbers ⋮ Unified treatment of Artin-type problems ⋮ Explicit Kummer theory for the rational numbers ⋮ The degree of Kummer extensions of number fields ⋮ Equality of orders of a set of integers modulo a prime ⋮ Kummer theory for multiquadratic or quartic cyclic number fields

Cites Work

• Reductions of algebraic integers
• Autour d'une conjecture de Serge Lang. (Around a conjecture by Serge Lang)
• Kummer theory on extensions of Abelian varieties by tori
• Detecting linear dependence by reduction maps
• Multiplicative Order and Frobenius Symbol for the Reductions of Number Fields
• Abelian binomials, power residues and exponential congruences
• Criterion for a field to be abelian
• Artin's Primitive Root Conjecture – A Survey
• Galois descent in Galois theories
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