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Softcover ISBN:  9780821846483 
Product Code:  CONM/493 
List Price:  $130.00 
MAA Member Price:  $117.00 
AMS Member Price:  $104.00 
eBook ISBN:  9780821881729 
Product Code:  CONM/493.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
Softcover ISBN:  9780821846483 
eBook ISBN:  9780821881729 
Product Code:  CONM/493.B 
List Price:  $255.00 $192.50 
MAA Member Price:  $229.50 $173.25 
AMS Member Price:  $204.00 $154.00 

Book DetailsContemporary MathematicsVolume: 493; 2009; 408 ppMSC: Primary 11; 12; 14; 19; 20;
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 2007.
The theory of quadratic forms is closely connected with a broad spectrum of areas in algebra and number theory. The articles in this volume deal mainly with questions from the algebraic, geometric, arithmetic, and analytic theory of quadratic forms, and related questions in algebraic group theory and algebraic geometry.
ReadershipGraduate students and research mathematicians interested in quadradic forms (and their applications in algebra), number theory, and algebraic geometry.

Table of Contents

Articles

Roberto Aravire and Bill Jacob — $H^1(X,\nu )$ of conics and Witt kernels in characteristic 2 [ MR 2537090 ]

Karim Johannes Becher and David B. Leep — Pythagoras numbers and quadratic field extensions [ MR 2537091 ]

AnneMarie Bergé and Jacques Martinet — On perfection relations in lattices [ MR 2537092 ]

Siegfried Böcherer, Yumiko Hironaka and Fumihiro Sato — Linear independence of local densities of quadratic forms and its application to the theory of Siegel modular forms [ MR 2537093 ]

M. Dickmann and F. Miraglia — Representation of reduced special groups in algebras of continuous functions [ MR 2537094 ]

T. D. Browning and R. Dietmann — Solubility of Fermat equations [ MR 2537095 ]

A. G. Earnest and Robert W. Fitzgerald — Multiplicative properties of integral binary quadratic forms [ MR 2537096 ]

Lenny Fukshansky — Effective structure theorems for symplectic spaces via height [ MR 2537097 ]

Skip Garibaldi — Orthogonal involutions on algebras of degree 16 and the Killing form of $E_8$ [ MR 2537098 ]

Stefan Gille — The first Zariski cohomology group of the Witt sheaf over a split simply connected simple algebraic group [ MR 2537099 ]

Paweł Gładki and Murray Marshall — On families of testing formulae for a pp formula [ MR 2537100 ]

Tomoyoshi Ibukiyama and Satoshi Wakatsuki — Siegel modular forms of small weight and the Witt operator [ MR 2537101 ]

Nikita A. Karpenko — On isotropy of quadratic pair [ MR 2537102 ]

Manfred Knebusch — Specialization of forms in the presence of characteristic 2: first steps [ MR 2537103 ]

Winfried Kohnen — Representation of integers by special positive definite integral quadratic forms [ MR 2537104 ]

Ahmed Laghribi and Pasquale Mammone — Hyperisotropy of bilinear forms in characteristic 2 [ MR 2537105 ]

David B. Leep — A historical view of the Pythagoras numbers of fields [ MR 2537106 ]

Michał Machura and Katarzyna Osiak — The extensions of $\Bbb R$places and application [ MR 2537107 ]

Alexander S. Merkurjev — Essential dimension [ MR 2537108 ]

R. Parimala, V. Suresh and J.P. Tignol — On the Pfister number of quadratic forms [ MR 2537109 ]

Rudolf Scharlau — Martin Kneser’s work on quadratic forms and algebraic groups [ MR 2537110 ]

Achill Schürmann — Enumerating perfect forms [ MR 2537111 ]

NilsPeter Skoruppa — Reduction mod $l$ of theta series of level $l^n$ [ MR 2537112 ]

Lynne H. Walling — On a reciprocity theorem of Gauss [ MR 2537113 ]

Takao Watanabe and Ryusuke Yoshimitsu — A bound of the number of reduced Arakelov divisors of a number field [ MR 2537114 ]


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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 2007.
The theory of quadratic forms is closely connected with a broad spectrum of areas in algebra and number theory. The articles in this volume deal mainly with questions from the algebraic, geometric, arithmetic, and analytic theory of quadratic forms, and related questions in algebraic group theory and algebraic geometry.
Graduate students and research mathematicians interested in quadradic forms (and their applications in algebra), number theory, and algebraic geometry.

Articles

Roberto Aravire and Bill Jacob — $H^1(X,\nu )$ of conics and Witt kernels in characteristic 2 [ MR 2537090 ]

Karim Johannes Becher and David B. Leep — Pythagoras numbers and quadratic field extensions [ MR 2537091 ]

AnneMarie Bergé and Jacques Martinet — On perfection relations in lattices [ MR 2537092 ]

Siegfried Böcherer, Yumiko Hironaka and Fumihiro Sato — Linear independence of local densities of quadratic forms and its application to the theory of Siegel modular forms [ MR 2537093 ]

M. Dickmann and F. Miraglia — Representation of reduced special groups in algebras of continuous functions [ MR 2537094 ]

T. D. Browning and R. Dietmann — Solubility of Fermat equations [ MR 2537095 ]

A. G. Earnest and Robert W. Fitzgerald — Multiplicative properties of integral binary quadratic forms [ MR 2537096 ]

Lenny Fukshansky — Effective structure theorems for symplectic spaces via height [ MR 2537097 ]

Skip Garibaldi — Orthogonal involutions on algebras of degree 16 and the Killing form of $E_8$ [ MR 2537098 ]

Stefan Gille — The first Zariski cohomology group of the Witt sheaf over a split simply connected simple algebraic group [ MR 2537099 ]

Paweł Gładki and Murray Marshall — On families of testing formulae for a pp formula [ MR 2537100 ]

Tomoyoshi Ibukiyama and Satoshi Wakatsuki — Siegel modular forms of small weight and the Witt operator [ MR 2537101 ]

Nikita A. Karpenko — On isotropy of quadratic pair [ MR 2537102 ]

Manfred Knebusch — Specialization of forms in the presence of characteristic 2: first steps [ MR 2537103 ]

Winfried Kohnen — Representation of integers by special positive definite integral quadratic forms [ MR 2537104 ]

Ahmed Laghribi and Pasquale Mammone — Hyperisotropy of bilinear forms in characteristic 2 [ MR 2537105 ]

David B. Leep — A historical view of the Pythagoras numbers of fields [ MR 2537106 ]

Michał Machura and Katarzyna Osiak — The extensions of $\Bbb R$places and application [ MR 2537107 ]

Alexander S. Merkurjev — Essential dimension [ MR 2537108 ]

R. Parimala, V. Suresh and J.P. Tignol — On the Pfister number of quadratic forms [ MR 2537109 ]

Rudolf Scharlau — Martin Kneser’s work on quadratic forms and algebraic groups [ MR 2537110 ]

Achill Schürmann — Enumerating perfect forms [ MR 2537111 ]

NilsPeter Skoruppa — Reduction mod $l$ of theta series of level $l^n$ [ MR 2537112 ]

Lynne H. Walling — On a reciprocity theorem of Gauss [ MR 2537113 ]

Takao Watanabe and Ryusuke Yoshimitsu — A bound of the number of reduced Arakelov divisors of a number field [ MR 2537114 ]