Arithmetic of Quadratic Forms
The aim of this book is to provide an introduction to quadratic forms that builds from basics up to the most recent results. Professor Kitaoka is well know for his work in this area, and in this book he covers many aspects of the subject, including lattice theory, Siegel's formula, and some results involving tensor products of positive definite quadratic forms. The reader is required to have only a knowledge of algebraic number fields, making this book ideal for graduate students and researchers wishing for an insight into quadratic forms.
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2-dimensional a)-maximal algebraic number field anisotropic Applying Lemma assertion assume assumption bilinear form Clifford algebra completes the proof contradicts Corollary decomposition define denote E-type element field F finite set follows Galois extension gen(L hence holds homomorphism hyperbolic plane hyperbolic space implies indecomposable induction hypothesis isometry isometry classes isotropic lattice of E-type linear mapping matrix min(L modular Moreover natural number non-zero orthogonal basis orthogonal sum positive definite quadratic positive lattice positive number previous lemma prime number Problem Proposition 5.6.1 prove Q(vi quadratic forms quadratic module rankM rational number regular quadratic lattice regular quadratic space resp set of representatives Siegel space over Q submodule subset subspace sufficiently close Suppose surjective symmetric bilinear Theorem unimodular lattice unramified verify virtue weighted graph write yields