Arithmetic of Quadratic Forms
Cambridge University Press, 29 avr. 1999 - 270 pages
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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a₁ algebraic anisotropic Applying assertion assume assumption B(vi basis bilinear called chapter clear completes the proof condition consider contains contradicts Corollary decomposition define denote dependent E-type easy element equal Exercise exists extension field F fixed follows gen(L give given hence holds hyperbolic plane implies indecomposable independent induction infinite integer isometry isotropic L₁ Lemma linear M₁ mapping matrix maximal means module Moreover N₁ orthogonal positive definite positive lattice prime primitive Problem Proposition prove quadratic forms rank regular quadratic lattice regular quadratic space represented respectively satisfies scaling side Similarly space over Q submodule sufficiently close sufficiently large Suppose symmetric Theorem theory u₁ unimodular v₁ vector verify virtue W₁ write yields