Rational Quadratic Forms

a₁ a₂ algebraic number fields anisotropic arbitrarily close autometry b₁ b₂ basis binary forms c₁ Chapter 9 clearly coefficients concludes the proof condition Corollary defined definite forms denote dimension e₁ e₂ elements equivalence classes example f₁ f₂ finite number finite set follows form f form of determinant Further given h₁ Hasse Principle Hence implies indefinite integral automorphs integral vector integrally equivalent isotropic lattice Let f Let f(x linear matrix modulo notation Note orthogonal orthogonal group p-adic unit P₁ Pell's equation positive definite positive integer primitive integral principal ideal domain proof of Theorem properly equivalent properties prove quadratic forms quadratic space rational regular quadratic s₁ satisfies Section set of primes Show Siegel solution Spin(V spinor genera spinor genus spinor norm subgroup ternary form Theorem 3.1 theory u₁ u₂ unimodular V₁ variables x₁ Z-equivalent Z-lattice