On integral representations by totally positive ternary quadratic forms (Q5939702)
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 integral representations by totally positive ternary quadratic forms |
scientific article; zbMATH DE number 1626604
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On integral representations by totally positive ternary quadratic forms |
scientific article; zbMATH DE number 1626604 |
Statements
On integral representations by totally positive ternary quadratic forms (English)
0 references
30 July 2001
0 references
ternary quadratic form
0 references
quadratic number field
0 references
quaternion order
0 references
0 references
The author studies totally definite ternary quadratic forms over the ring \(R\) of integers of a totally real quadratic number field. NEWLINENEWLINENEWLINEModifying the methods of \textit{J. Brzezinski} [J. Reine Angew. Math. 402, 199--210 (1989; Zbl 0674.16003)] she gets a quantitative formula for the number of representations of \(N\) in terms of the class number of \(R[\sqrt{-cN}]\) with \(c\) depending only on the considered form. NEWLINENEWLINENEWLINEIn the case of \(\mathbb Q(\sqrt{5})\) the algebraic proof of the classical result of H. Maass and the formulae for the number of representations are given.
0 references
