Orthogonal splitting and class numbers of quadratic forms (Q758504)

The author's main result may be explained as follows. Let \(f\) be an \(n\)-ary quadratic form over the integer ring of an algebraic number field \(F\), denote by \(h\) the number of classes in the genus of \(f\), and suppose that \(f\) is definite. Then \[ h\geq p([(n-5)/16]), \] where \(p\) is the partition function. This is proved by first showing (for either definite or indefinite \(f\)) that the genus contains a disjoint form if \(n\) is large enough.