Exceptional integers for genera of integral ternary positive definite quadratic forms
Let \((L,q)\) be a \(\mathbb{Z}\)-lattice of rank 3 with integral positive definite quadratic form. Then all sufficiently large integers that are represented primitively by some lattice in the spinor genus of \((L,q)\) are represented by all lattices in that spinor genus [\textit{W. Duke} and \textit{R. Schulze-Pillot}, Invent. Math. 99, 49-57 (1990; Zbl 0692.10020)]. The theorems of this article imply a slightly sharper characterization of the set of exceptional integers that are represented by some forms in the genus of \(L\) but not by all of them. This is explained in detail in the article under review. Furthermore the question of effectivity and results for primitive representations are described.
scientific article; zbMATH DE number 1436093