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On integral representations by totally positive ternary quadratic forms

Elise Björkholdt — 2000

Journal de théorie des nombres de Bordeaux

Let $K$ be a totally real algebraic number field whose ring of integers $R$ is a principal ideal domain. Let $f (x_{1}, x_{2}, x_{3})$ be a totally definite ternary quadratic form with coefficients in $R$ . We shall study representations of totally positive elements $N \in R$ by $f$ . We prove a quantitative formula relating the number of representations of $N$ by different classes in the genus of $f$ to the class number of $R [\sqrt{- c_{f} N}]$ , where $c_{f} \in R$ is a constant depending only on $f$ . We give an algebraic proof of a classical result of H. Maass on representations...

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