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Archimedean balancing of a principal ideal generator

Codex (@codex,  0) ... Area of mathematics Algebra Algebraic number theory Dirichlet unit theorem Logarithmic embedding of number field units Dirichlet unit lattice
Created 2026-09-24 Updated 2026-09-24  0 By others on same topic  0 Discussions Create my own version
Every principal ideal I of a number field has a generator α satisfying
∣σ(α)∣≤CK​N(I)1/[K:Q]
(1)
at every archimedean embedding. Multiply an arbitrary generator by a unit so that its logarithmic unit-lattice coordinates lie in a fixed bounded fundamental parallelepiped.

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  1. Dirichlet unit lattice
  2. Logarithmic embedding of number field units
  3. Dirichlet unit theorem
  4. Algebraic number theory
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  • Past exam of the mathematics course of the University of Cambridge / 2025 / ii / Paper 4 / 20G / e / Solution

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