Algebraic and Arithmetic Theory of Quadratic Forms, December 1319, 2007, Frutillar, Chile.;This volume presents a collection of articles that are based on talks delivered at the International Conference on the Algebraic and Arithmetic Theory of Quadratic Forms held in Frutillar, Chile in December 2007P. [4] of cover.

Includes bibliographical references.

^1(X,\nu ) of conics and Witt kernels in characteristic 2 ; Pythagoras numbers and quadratic field extensions ; On perfection relations in lattices ; Linear independence of local densities of quadratic forms and its application to the theory of Siegel modular forms ; Representation of reduced special groups in algebras of continuous functions ; Solubility of Fermat equations ; Multiplicative properties of integral binary quadratic forms ; Effective structure theorems for symplectic spaces via height ; Orthogonal involutions on algebras of degree 16 and the Killing form of _8 ; The first Zariski cohomology group of the Witt sheaf over a split simply connected simple algebraic group ; On families of testing formulae for a pp formula ; Siegel modular forms of small weight and the Witt operator ; On isotropy of quadratic pair ; Specialization of forms in the presence of characteristic 2: first steps ; Representation of integers by special positive definite integral quadratic forms ; Hyperisotropy of bilinear forms in characteristic 2 ; A historical view of the Pythagoras numbers of fields ; The extensions of Bbb R laces and application ; Essential dimension ; On the Pfister number of quadratic forms ; Martin Kneser's work on quadratic forms and algebraic groups ; Enumerating perfect forms ; Reduction mod of theta series of level ^n ; On a reciprocity theorem of Gauss ; A bound of the number of reduced Arakelov divisors of a number field Roberto Aravire and Bill Jacob ; Karim Johannes Becher and David B Leep ; AnneMarie Berge and Jacques Martinet ; Siegfried Bocherer Yumiko Hironaka and Fumihiro Sato ; M Dickmann and F Miraglia ; T D Browning and R Dietmann ; A G Earnest and Robert W Fitzgerald ; Lenny Fukshansky ; Skip Garibaldi ; Stefan Gille ; Pawe Gadki and Murray Marshall ; Tomoyoshi Ibukiyama and Satoshi Wakatsuki ; Nikita A Karpenko ; Manfred Knebusch ; Winfried Kohnen ; Ahmed Laghribi and Pasquale Mammone ; David B Leep ; Micha Machura and Katarzyna Osiak ; Alexander S Merkurjev ; R Parimala V Suresh and JP Tignol ; Rudolf Scharlau ; Achill Schurmann ; NilsPeter Skoruppa ; Lynne H Walling ; Takao Watanabe and Ryusuke Yoshimitsu