Reductions of algebraic integers

DOI10.1016/j.jnt.2016.03.001zbMath1411.11120OpenAlexW2344907887MaRDI QIDQ290045

Antonella Perucca, Christophe Debry

Publication date: 1 June 2016

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

Full work available at URL: https://doi.org/10.1016/j.jnt.2016.03.001

zbMATH Keywords

reductiondensityKummer theorynumber fieldalgebraic integer

Mathematics Subject Classification ID

Other number fields (11R21) Algebraic number theory computations (11Y40) Distribution of prime ideals (11R44) Cyclotomic extensions (11R18)

Related Items (13)

Divisibility parameters and the degree of Kummer extensions of number fields ⋮ EXPLICIT KUMMER THEORY FOR QUADRATIC FIELDS ⋮ Kummer theory for number fields via entanglement groups ⋮ Divisibility conditions on the order of the reductions of algebraic numbers ⋮ Unified treatment of Artin-type problems ⋮ Explicit Kummer theory for the rational numbers ⋮ Multiplicative Order and Frobenius Symbol for the Reductions of Number Fields ⋮ Addendum to: ``Reductions of algebraic integers ⋮ REDUCTIONS OF POINTS ON ALGEBRAIC GROUPS ⋮ Kummer theory for number fields and the reductions of algebraic numbers ⋮ The degree of Kummer extensions of number fields ⋮ Kummer theory for multiquadratic or quartic cyclic number fields ⋮ Reductions of one-dimensional tori

Uses Software

• SageMath

Cites Work

• The order of the reductions of an algebraic integer
• Über die Dichte der Primzahlen \(p\), für die eine vorgegebene ganzrationale Zahl \(a\neq 0\) von durch eine vorgegebene Primzahl \(l\neq 2\) teilbarer bzw. unteilbarer Ordnung \(\mod p\) ist
• Über die Dichte der Primzahlen \(p\), für die eine vorgegebene ganzrationale Zahl \(a\neq 0\) von gerader bzw. ungerader Ordnung \(\mod p\) ist
• Galois theory of iterated endomorphisms
• Artin's Primitive Root Conjecture – A Survey
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