Arithmetic of Quadratic FormsCambridge 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. |
Table des matières
III | 1 |
V | 3 |
VI | 12 |
VII | 20 |
VIII | 24 |
IX | 32 |
X | 33 |
XII | 42 |
XXV | 129 |
XXVI | 134 |
XXVII | 147 |
XXVIII | 151 |
XXIX | 157 |
XXX | 164 |
XXXI | 169 |
XXXII | 173 |
XIII | 47 |
XV | 52 |
XVI | 56 |
XVII | 64 |
XVIII | 70 |
XX | 71 |
XXI | 79 |
XXII | 86 |
XXIII | 92 |
XXIV | 94 |
XXXIII | 189 |
XXXIV | 190 |
XXXV | 199 |
XXXVI | 217 |
XXXVII | 222 |
XXXVIII | 239 |
XXXIX | 250 |
| 263 | |
| 269 | |
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Expressions et termes fréquents
a)-maximal a₁ algebraic number field anisotropic assertion assume assumption B(ui B(vi b₁ Co(V completes the proof condition contradicts Corollary decomposition define denote E-type e₁ element exists field F finite set follows Galois extension gen(L hence holds hyperbolic plane hyperbolic space implies indecomposable isometry isotropic K₁ L₁ Lemma linear mapping M₂ matrix min(L mod 2p N₁ N₂ natural number O+(V orthogonal basis orthogonal sum positive definite positive definite quadratic positive lattice positive number primitive Proposition 5.6.1 prove quadratic forms QX)² rank M₁ regular quadratic lattice regular quadratic space represented resp satisfies space over Q spinor ßp(M submodule subspace sufficiently close sufficiently large Suppose surjective symmetric bilinear Theorem totally real u₁ unimodular lattice v₁ vector verify virtue W₁ weighted graph yields