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Results tagged with number-fields
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user 95241
14
votes
1
answer
1k
views
How Dirichlet proved Dirichlet's unit theorem for general number fields?
For a general number field $K$, Dirichlet's unit theorem states that the unit group of the ring of integers of $K$ is a finitely generated group of rank $r_1+r_2-1$.
It seems that standard algebraic n …
- 1,053
9
votes
1
answer
513
views
class number of prime degree field with prime conductor
Let $K$ be an finite abelian extension of $\mathbf{Q}$ conductor $p$, where $p$ is an odd prime. That is, $K \subset \mathbf{Q}(\mu_ p)$, the $p$-th cyclotomic field. Let $h_K$ be the class number of …
- 1,053