A characterization of tame Hilbert-symbol equivalence
We investigate the almost regular positive definite integral quaternary quadratic forms. In particular, we show that every such form is -anisotropic for at most one prime number . Moreover, for a prime there is an almost regular -anisotropic quaternary quadratic form if and only if . We also study the genera containing some almost regular -anisotropic quaternary form. We show several finiteness results concerning the families of these genera and give effective criteria for almost regularity....
We improve the known upper bound of the dimension of an indecomposable unimodular lattice whose shadow has the third largest possible length, .