Number-field translations

Core idea

Construct the Archimedean torus and its character lattice before comparing one translation with the joint additive action of the ring of integers.

Prerequisite doorway

• Number field
• Ring of integers of a number field
• Field trace
• Pontryagin dual

Reading path

• Archimedean algebra of a number field
• Minkowski embedding of a number field
• Archimedean trace pairing
• Codifferent of a number field
• Number-field torus
• Characters of a number-field torus
• Ergodicity of a single number-field translation
• Ergodic translation action of the ring of integers
• Translations on the Gaussian-integer torus

Return to Ergodic theory.