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Arithmetic of Quadratic Forms (Springer Monographs in Mathematics) - Softcover
Buch 73 von 187: Springer Monographs in Mathematics
Inhaltsangabe
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.
Die Inhaltsangabe kann sich auf eine andere Ausgabe dieses Titels beziehen.
Über die Autorin bzw. den Autor
Goro Shimura is currently a professor emeritus of mathematics at Princeton University.
Von der hinteren Coverseite
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.
„Über diesen Titel“ kann sich auf eine andere Ausgabe dieses Titels beziehen.
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Zustand: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. -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. Bestandsnummer des Verkäufers 4197613
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Taschenbuch. Zustand: 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. 252 pp. Englisch. Bestandsnummer des Verkäufers 9781461426189
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Taschenbuch. Zustand: Neu. Arithmetic of Quadratic Forms | Goro Shimura | Taschenbuch | Springer Monographs in Mathematics | xii | Englisch | 2012 | Springer | EAN 9781461426189 | Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu. Bestandsnummer des Verkäufers 106298075
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Taschenbuch. Zustand: 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. Bestandsnummer des Verkäufers 9781461426189
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Taschenbuch. Zustand: Neu. This item is printed on demand - Print on Demand Titel. Neuware -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.Springer-Verlag KG, Sachsenplatz 4-6, 1201 Wien 252 pp. Englisch. Bestandsnummer des Verkäufers 9781461426189
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