ISBN10: 1441917314, ISBN13: 9781441917317, [publisher: Springer US] Hardcover Neubindung, Buchschnitt leicht verkürzt 5902868/12
[Trebbin, Germany] [Publication Year: 2010]

ISBN10: 1441917314, ISBN13: 9781441917317, [publisher: Springer US] Hardcover Neubindung, Buchschnitt leicht verkürzt 5902868/12
[Trebbin, Germany] [Publication Year: 2010]

ISBN10: 1441917314, ISBN13: 9781441917317, [publisher: Springer New York] Hardcover 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 ...
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ISBN10: 1441917314, ISBN13: 9781441917317, [publisher: Springer] Hardcover
[Bayonne, NJ, U.S.A.] [Publication Year: 2010]
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ISBN10: 1441917314, ISBN13: 9781441917317, [publisher: Springer New York] Hardcover 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 ...
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New York, NY Springer 2010 2010 ed. Hard cover New. Sewn binding. Cloth over boards. 238 p. Contains: Unspecified. Springer Monographs in Mathematics.

ISBN10: 1441917314, ISBN13: 9781441917317, [publisher: Springer] Hardcover
[Miami, FL, U.S.A.] [Publication Year: 2010]