Quadratic Forms--algebra, Arithmetic, and Geometry

by Baeza, Ricardo; Chan, Wai Kiu; Hoffmann, Detlev W.; Schulze-Pillot, Rainer

• ISBN13: 9780821846483
• ISBN10: 0821846485
• Format: Paperback
• Copyright: 2009-09-13
• Publisher: Amer Mathematical Society

Summary

$H^1(X,\nu)$ of conics and Witt kernels in characteristic $2$ by R. Aravire and B. Jacob Pythagoras numbers and quadratic field extensions by K.J. Becher and D. B. Leep On perfection relations in lattices by A.-M. Berge and J. Martinet Linear independence of local densities of quadratic forms and its application to the theory of Siegel modular forms by S. Bocherer, Y. Hironaka, and F. Sato Representation of reduced special groups in algebras of continuous functions by M. Dickmann and F. Miraglia Solubilty of Fermat equations by T. D. Browning and R. Dietmann Multiplicative properties of integral binary quadratic forms by A. G. Earnest and R. W. Fitzgerald Effective structure theorems for symplectic spaces via height by L. Fukshansky Orthogonal involutions on algebras of degree 16 and the Killing form of $E_8$ (Appendix A: Non-hyperbolicity of orthogonal involutions) by S. Garibaldi and K. Zainoulline The first Zariski cohomology group of the Witt sheaf over a split simply connected simple algebraic group by S. Gille On families of testing formulae for a pp formula by P. Gladki and M. Marshall Siegel modular forms of a small weight and the Witt operator by T. Ibukiyama and S. Wakatsuki On isotropy of quadratic pairs by N. A. Karpenko Specialization of forms in the presence of characteristic 2: first steps by M. Knebusch Representation of integers by special positive definite integral quadratic forms by W. Kohnen Hyper-isotropy of bilinear forms in characteristic 2 by A. Laghribi and P. Mammone A historical view of the Pythagoras numbers of fields by D. B. Leep The extensions of $\mathbb R$-places and application by M. Machura and K. Osiak Essential dimension by A. S. Merkurjev On the Pfister number of quadratic forms by R. Parimala, V. Suresh, and J.-P. Tignol Martin Kneser's work on quadratic forms and algebraic groups by R. Scharlau Enumerating perfect forms by A. Schurmann Reduction mod $\ell$ of Theta series of level $\ell^n$ by N.-P. Skoruppa On a reciprocity theorem of Gauss by L. H. Walling A bound of the number of reduced Arakelov divisors of a number field by T. Watanabe and R. Yoshimitsu

Table of Contents

$H^1(X,\nu)$ 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

Solubilty 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 $E_8$ (Appendix A: Non-hyperbolicity of orthogonal involutions)

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 a small weight and the Witt operator

On isotropy of quadratic pairs

Specialization of forms in the presence of characteristic 2: first steps

Representation of integers by special positive definite integral quadratic forms

Hyper-isotropy of bilinear forms in characteristic 2

A historical view of the Pythagoras numbers of fields

The extensions of $\mathbb R$-places 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 $\ell$ of Theta series of level $\ell^n$

On a reciprocity theorem of Gauss

A bound of the number of reduced Arakelov divisors of a number field

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