Dirichlet unit lattice

The logarithms of a fundamental system of

r + s - 1

units form a basis of the hyperplane

H = {x \in R^{r + s} : x_{1} + \dots + x_{r + s} = 0},

and their integer span is a full lattice in

H

.

Table of contents
- Archimedean balancing of a principal ideal generator Dirichlet unit lattice

Archimedean balancing of a principal ideal generator

Every principal ideal

I

of a number field has a generator

α

satisfying

∣ σ (α) ∣ \leq C_{K} N (I)^{1/ [K : Q]}

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.

 Ancestors (7)

 Incoming links (1)

Past exam of the mathematics course of the University of Cambridge / 2025 / ii / Paper 4 / 20G / c / Solution

 View article source

 Discussion (0)

There are no discussions about this article yet.

 Articles by others on the same topic (0)

There are currently no matching articles.

  See all articles in the same topic Create my own version