Spinor norms of local integral rotations. I
The spinor norms of integral rotations on a modular quadratic form over a local field are determined. Whenever possible, these results are expressed in convenient closed forms. Two key facts are used: (i) the O'Meara-Pollak theorem that the integral orthogonal group \(O(L)\) on a modular lattice \(L\) is almost always equal to the subgroup \(S(L)\) generated by the symmetries, and (ii) a duality lemma for non-square units by means of the quadratic defect function (see Lemma 3). For Part II (jointly with A. G. Earnest) see [Pac. J. Math. 61, 71--86 (1975; Zbl 0334.10012)].
scientific article; zbMATH DE number 3443711