Algebraic number theory MOC
Algebraic number theory is the study of integers, i.e. number theory, via the study of things bigger than the integers, i.e. ring theory and field theory. The central objects are the number field and its ring of integers. In particular, we study
- Quadratic field with the Quadratic integers.
- Cyclotomic field with the Cyclotomic integers.
Geometry of numbers
- Minkowski’s convex body theorem
- Minkowski embedding, Minkowski’s bound
- Logarithmic embedding, Dirichlet’s unit theorem