Integral spinor norms in dyadic local fields. I (Q1314923)

The best bound about the orders of the discriminants of integral quadratic forms is given which makes the spinor norms of orthogonal groups of these integral quadratic forms over arbitrary dyadic local fields contain the whole units of the field. As an application, the results are applied to improve the sufficient condition for the class number of an indefinite quadratic form over the ring of integers of a number field to be a divisor of the class number of the field. [Part II, cf. Acta Arith. 63, 223-232 (1993; Zbl 0780.11017)].