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Logarithmic embedding of number field units

Choose the real embeddings

σ_{i}

and one embedding

τ_{j}

from each complex-conjugate pair. The weighted logarithmic embedding is

Log (u) = (lo g ∣ σ_{1} u ∣, \dots, lo g ∣ σ_{r} u ∣, 2 lo g ∣ τ_{1} u ∣, \dots, 2 lo g ∣ τ_{s} u ∣) .

For a unit, the sum of these coordinates is

lo g ∣ N_{K / Q} (u) ∣ = 0

.

Table of contents 148 3
- Kernel of the logarithmic unit embedding Logarithmic embedding of number field units 47
- Dirichlet unit lattice Logarithmic embedding of number field units 68 1
  - Archimedean balancing of a principal ideal generator Dirichlet unit lattice 40

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