On the bounds for the fundamental units and the class numbers (Q2883270)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: On the bounds for the fundamental units and the class numbers |
scientific article; zbMATH DE number 6033794
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the bounds for the fundamental units and the class numbers |
scientific article; zbMATH DE number 6033794 |
Statements
11 May 2012
0 references
class number
0 references
real quadratic field
0 references
On the bounds for the fundamental units and the class numbers (English)
0 references
Let \(p\) be a prime with \(p\equiv 7 \pmod{8}\). Suppose that \(\varepsilon >1\) is the fundamental unit of the quadratic field \({\mathbb Q}(\sqrt{3p})\) and \(h\) its class number. The author proves the following nice result: \(\varepsilon^h <2^{p-1}\). The proof involves a classical argument.
0 references
