We obtain a characterization of the algebraic and quasi-algebraic norm forms in terms of their values at integer points. As a consequence, we get a bijective correspondence between this kind of forms and the compact orbits for the action of the maximal tori of any rank on the space of unimodular lattices in $\R^n$. The result is relevant to a conjecture of Cassels and Swinnerton-Dyer.
Characterization of digital $(0,m,3)$-nets and digital $(0,2)$-sequences in base $2$
Integer points and their orthogonal lattices
On the Density of Integer Points on Generalised Markoff-Hurwitz and Dwork Hypersurfaces
![QR code for arXiv:2212.09734 [math.NT]](http://oss.arxitics.com/images/favicon.svg)