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Algebraic and Arithmetic Theory of Quadratic Forms
Edited by: Ricardo Baeza, Universidad de Talca, Chile, John S. Hsia, Ohio State University, Columbus, OH, Bill Jacob, University of California, Santa Barbara, CA, and Alexander Prestel, University of Konstanz, Germany
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Contemporary Mathematics
2004; 350 pp; softcover
Volume: 344
ISBN-10: 0-8218-3441-X
ISBN-13: 978-0-8218-3441-1
List Price: US$98
Member Price: US$78.40
Order Code: CONM/344
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This proceedings volume contains papers presented at the International Conference on the algebraic and arithmetic theory of quadratic forms held in Talca (Chile).

The modern theory of quadratic forms has connections with a broad spectrum of mathematical areas including number theory, geometry, and K-theory. This volume contains survey and research articles covering the range of connections among these topics.

The survey articles bring readers up-to-date on research and open problems in representation theory of integral quadratic forms, the algebraic theory of finite square class fields, and developments in the theory of Witt groups of triangulated categories. The specialized articles present important developments in both the algebraic and arithmetic theory of quadratic forms, as well as connections to geometry and K-theory.

The volume is suitable for graduate students and research mathematicians interested in various aspects of the theory of quadratic forms.

Readership

Graduate students and research mathematicians interested in various aspects of the theory of quadratic forms.

Table of Contents

  • R. Aravire and B. Jacob -- The Milnor sequence for \(W_q\mathcal{F}(x)\) in characteristic 2 when \(\mathcal{F}\) is perfect
  • L. Arenas-Carmona -- Spinor norm for local skew-Hermitian forms
  • P. Balmer -- An introduction to triangular Witt groups and a survey of applications
  • W. K. Chan, A. G. Earnest, and B.-K. Oh -- Regularity properties of positive definite integral quadratic forms
  • W. K. Chan and M. I. Icaza -- Effective results on representations of quadratic forms
  • W. K. Chan and M. Peters -- Quaternary quadratic forms and Hilbert modular surfaces
  • M. Dickmann and A. Petrovich -- Real semigroups and abstract real spectra. I
  • M. Gaulter -- The role of characteristic vectors in the neighbour lattice process
  • L. J. Gerstein -- On representation by quadratic \(\mathbb{F}_q[x]\)-lattices
  • D. W. Hoffmann -- Diagonal forms of degree \(p\) in characteristic \(p\)
  • D. G. James -- Local densities and the representations of an integer by a definite quadratic form
  • M. Karoubi -- Periodicity of Hermitian K-theory and Milnor's K-groups
  • N. A. Karpenko -- Third proof of second gap in dimensions of quadratic forms from \(I^n\)
  • M.-H. Kim -- Recent developments on universal forms
  • W. Kohnen -- Special Siegel modular forms and singular series polynomials of quadratic forms
  • A. Laghribi -- Quasi-hyperbolicity of totally singular quadratic forms
  • D. B. Leep and T. L. Smith -- Witt kernels of triquadratic extensions
  • D. W. Lewis -- Anti-automorphisms of the second kind
  • J. Martinet -- Reduction modulo 2 and 3 of Euclidean lattices, II
  • M. Marshall -- The elementary type conjecture in quadratic form theory
  • A. Pfister -- On Hilbert's theorem about ternary quartics
  • R. Schulze-Pillot -- Representation by integral quadratic forms-A survey
  • R. Schulze-Pillot and F. Xu -- Representations by spinor genera of ternary quadratic forms
  • T. Watanabe -- A survey and a complement of fundamental Hermite constants
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