Articles liés à Arithmetic of Quadratic Forms
Arithmetic of Quadratic Forms - Couverture rigide
Livre 73 sur 184: Springer Monographs in Mathematics
Synopsis
This book is divided into two parts. The first part is preliminary and consists of algebraic number theory and the theory of semisimple algebras. There are two principal topics: classification of quadratic forms and quadratic Diophantine equations. The second topic is a new framework which contains the investigation of Gauss on the sums of three squares as a special case.To make the book concise, the author proves some basic theorems in number theory only in some special cases. However, the book is self-contained when the base field is the rational number field, and the main theorems are stated with an arbitrary number field as the base field. So the reader familiar with class field theory will be able to learn the arithmetic theory of quadratic forms with no further references.
Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.
À propos de la quatrième de couverture
This book is divided into two parts. The first part is preliminary and consists of algebraic number theory and the theory of semisimple algebras. There are two principal topics: classification of quadratic forms and quadratic Diophantine equations. The second topic is a new framework which contains the investigation of Gauss on the sums of three squares as a special case.To make the book concise, the author proves some basic theorems in number theory only in some special cases. However, the book is self-contained when the base field is the rational number field, and the main theorems are stated with an arbitrary number field as the base field. So the reader familiar with class field theory will be able to learn the arithmetic theory of quadratic forms with no further references.
Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.
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Arithmetic of Quadratic Forms (eng)
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Arithmetic of Quadratic Forms
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Arithmetic of Quadratic Forms (Springer Monographs in Mathematics)
Edité par
Springer 2010-06-30, 2010
ISBN 10 : 1441917314
ISBN 13 : 9781441917317
Neuf
Couverture rigide
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Arithmetic of Quadratic Forms (Springer Monographs in Mathematics)
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Arithmetic of Quadratic Forms
Edité par
Springer Nature Singapore Jun 2010, 2010
ISBN 10 : 1441917314
ISBN 13 : 9781441917317
Neuf
Couverture rigide
Vendeur : BuchWeltWeit Ludwig Meier e.K., Bergisch Gladbach, Allemagne
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Buch. Etat : Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -This book can be divided into two parts. The rst part is preliminary and consists of algebraic number theory and the theory of semisimple algebras. The raison d' etre of the book is in the second part, and so let us rst explain the contents of the second part. There are two principal topics: (A) Classi cation of quadratic forms; (B) Quadratic Diophantine equations. Topic (A) can be further divided into two types of theories: (a1) Classi cation over an algebraic number eld; (a2) Classi cation over the ring of algebraic integers. To classify a quadratic form over an algebraic number eld F, almost all previous authors followed the methods of Helmut Hasse. Namely, one rst takes in the diagonal form and associates an invariant to it at each prime spot of F, using the diagonal entries. A superior method was introduced by Martin Eichler in 1952, but strangely it was almost completely ignored, until I resurrected it in one of my recent papers. We associate an invariant to at each prime spot, which is the same as Eichler's, but we de ne it in a di erent and more direct way, using Cli ord algebras. In Sections 27 and 28 we give an exposition of this theory. At some point we need the Hasse norm theorem for a quadratic extension of a number eld, which is included in class eld theory. We prove it when the base eld is the rational number eld to make the book self-contained in that case. 238 pp. Englisch. N° de réf. du vendeur 9781441917317
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Arithmetic of Quadratic Forms
Edité par
Springer-Verlag New York Inc., US, 2010
ISBN 10 : 1441917314
ISBN 13 : 9781441917317
Neuf
Couverture rigide
Vendeur : Rarewaves.com USA, London, LONDO, Royaume-Uni
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Hardback. Etat : New. 2010 ed. This book can be divided into two parts. The ?rst part is preliminary and consists of algebraic number theory and the theory of semisimple algebras. The raison d'^ etre of the book is in the second part, and so let us ?rst explain the contents of the second part. There are two principal topics: (A) Classi?cation of quadratic forms; (B) Quadratic Diophantine equations. Topic (A) can be further divided into two types of theories: (a1) Classi?cation over an algebraic number ?eld; (a2) Classi?cation over the ring of algebraic integers. To classify a quadratic form ? over an algebraic number ?eld F, almost all previous authors followed the methods of Helmut Hasse. Namely, one ?rst takes ? in the diagonal form and associates an invariant to it at each prime spot of F, using the diagonal entries. A superior method was introduced by Martin Eichler in 1952, but strangely it was almost completely ignored, until I resurrected it in one of my recent papers. We associate an invariant to ? at each prime spot, which is the same as Eichler's, but we de?ne it in a di?erent and more direct way, using Cli?ord algebras. In Sections 27 and 28 we give an exposition of this theory. At some point we need the Hasse norm theorem for a quadratic extension of a number ?eld, which is included in class ?eld theory. We prove it when the base ?eld is the rational number ?eld to make the book self-contained in that case. N° de réf. du vendeur LU-9781441917317
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Arithmetic of Quadratic Forms
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Hardcover. Etat : Brand New. 1st edition. 237 pages. 9.25x6.50x0.75 inches. In Stock. This item is printed on demand. N° de réf. du vendeur __1441917314
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Arithmetic of Quadratic Forms
Edité par
Springer New York, 2010
ISBN 10 : 1441917314
ISBN 13 : 9781441917317
Neuf
Couverture rigide
Vendeur : moluna, Greven, Allemagne
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Etat : New. -Discusses algebraic number theory and the theory of semisimple algebras-Discusses classification of quadratic forms over the ring of algebraic integers-Discusses local class field theory-Presents a new framework of quadratic Diophantine equationsThis b. N° de réf. du vendeur 4172358
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Arithmetic of Quadratic Forms
Edité par
Springer New York, 2010
ISBN 10 : 1441917314
ISBN 13 : 9781441917317
Neuf
Couverture rigide
Vendeur : AHA-BUCH GmbH, Einbeck, Allemagne
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Buch. Etat : Neu. Druck auf Anfrage Neuware - Printed after ordering - This book can be divided into two parts. The rst part is preliminary and consists of algebraic number theory and the theory of semisimple algebras. The raison d' etre of the book is in the second part, and so let us rst explain the contents of the second part. There are two principal topics: (A) Classi cation of quadratic forms; (B) Quadratic Diophantine equations. Topic (A) can be further divided into two types of theories: (a1) Classi cation over an algebraic number eld; (a2) Classi cation over the ring of algebraic integers. To classify a quadratic form over an algebraic number eld F, almost all previous authors followed the methods of Helmut Hasse. Namely, one rst takes in the diagonal form and associates an invariant to it at each prime spot of F, using the diagonal entries. A superior method was introduced by Martin Eichler in 1952, but strangely it was almost completely ignored, until I resurrected it in one of my recent papers. We associate an invariant to at each prime spot, which is the same as Eichler's, but we de ne it in a di erent and more direct way, using Cli ord algebras. In Sections 27 and 28 we give an exposition of this theory. At some point we need the Hasse norm theorem for a quadratic extension of a number eld, which is included in class eld theory. We prove it when the base eld is the rational number eld to make the book self-contained in that case. N° de réf. du vendeur 9781441917317
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Arithmetic of Quadratic Forms (Springer Monographs in Mathematics)
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