Dirichlet’s unit theorem


occur in

Let K be a number fieldMathworldPlanetmath, and let 𝒪K be its ring of integersMathworldPlanetmath. Then


Here 𝒪K* is the group of units of 𝒪K, μ(K) is the finite cyclic group of the roots of unityMathworldPlanetmath in 𝒪K*, r is the number of real embeddings K, and 2s is the number of non-real complex embeddings K (which occur in complex conjugateMathworldPlanetmath pairs, so s is an integer).

Title Dirichlet’s unit theorem
Canonical name DirichletsUnitTheorem
Date of creation 2013-03-22 13:22:42
Last modified on 2013-03-22 13:22:42
Owner yark (2760)
Last modified by yark (2760)
Numerical id 10
Author yark (2760)
Entry type Theorem
Classification msc 11R04
Classification msc 11R27
Related topic RegulatorMathworldPlanetmath