Die Geschlechterzahl beliebiger Ordnungen in reell-quadratischen Zahlk�rpern

Symmetric Matrices: Theory and Applications

“…For the injective affine map Φ(x, y) [18], prop.2.6). 17 In case β = 0 there exists (x, y) ∈ P with xy = 0 by the fact above. Otherwise (x, y) := (β, −1) does it.…”

“…there is no "quadratic polynomial" 16 Quadrics with internal centre show a very special geometry: s. [18], lem.2.3b)! 17 but not necessarily Q = Φ(P ) q + l + γ : V ′ → K (like in (4.1)) that defines Q on any other vector space V ′ ⊃ V . b) In case |K| > 5, for linearly independent a, b of a quadric at zero centre o / ∈ Q there is a point c = xa+yb ∈ Q with xy = 0 according to Proposition 4.3b).…”