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Arithmetic and Analytic Theories of Quadratic Forms and Clifford Groups
 
Goro Shimura Princeton University, Princeton, NJ
Arithmetic and Analytic Theories of Quadratic Forms and Clifford Groups
Softcover ISBN:  978-1-4704-1562-4
Product Code:  SURV/109.S
List Price: $129.00
MAA Member Price: $116.10
AMS Member Price: $103.20
eBook ISBN:  978-1-4704-1336-1
Product Code:  SURV/109.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Softcover ISBN:  978-1-4704-1562-4
eBook: ISBN:  978-1-4704-1336-1
Product Code:  SURV/109.S.B
List Price: $254.00 $191.50
MAA Member Price: $228.60 $172.35
AMS Member Price: $203.20 $153.20
Arithmetic and Analytic Theories of Quadratic Forms and Clifford Groups
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Arithmetic and Analytic Theories of Quadratic Forms and Clifford Groups
Goro Shimura Princeton University, Princeton, NJ
Softcover ISBN:  978-1-4704-1562-4
Product Code:  SURV/109.S
List Price: $129.00
MAA Member Price: $116.10
AMS Member Price: $103.20
eBook ISBN:  978-1-4704-1336-1
Product Code:  SURV/109.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Softcover ISBN:  978-1-4704-1562-4
eBook ISBN:  978-1-4704-1336-1
Product Code:  SURV/109.S.B
List Price: $254.00 $191.50
MAA Member Price: $228.60 $172.35
AMS Member Price: $203.20 $153.20
  • Book Details
     
     
    Mathematical Surveys and Monographs
    Volume: 1092004; 275 pp
    MSC: Primary 11; 15; 22;

    In this book, award-winning author Goro Shimura treats new areas and presents relevant expository material in a clear and readable style. Topics include Witt's theorem and the Hasse principle on quadratic forms, algebraic theory of Clifford algebras, spin groups, and spin representations. He also includes some basic results not readily found elsewhere.

    The two principle themes are:

    (1) Quadratic Diophantine equations;

    (2) Euler products and Eisenstein series on orthogonal groups and Clifford groups.

    The starting point of the first theme is the result of Gauss that the number of primitive representations of an integer as the sum of three squares is essentially the class number of primitive binary quadratic forms. Presented are a generalization of this fact for arbitrary quadratic forms over algebraic number fields and various applications. For the second theme, the author proves the existence of the meromorphic continuation of a Euler product associated with a Hecke eigenform on a Clifford or an orthogonal group. The same is done for an Eisenstein series on such a group.

    Beyond familiarity with algebraic number theory, the book is mostly self-contained. Several standard facts are stated with references for detailed proofs.

    Goro Shimura won the 1996 Steele Prize for Lifetime Achievement for “his important and extensive work on arithmetical geometry and automorphic forms”.

    Readership

    Graduate students and research mathematicians interested in number theory and algebraic groups.

  • Table of Contents
     
     
    • Chapters
    • I. Algebraic theory of quadratic forms, Clifford algebras, and spin groups
    • II. Quadratic forms, Clifford algebras, and spin groups over a local or global field
    • III. Quadratic Diophantine equations
    • IV. Groups and symmetric spaces over R
    • V. Euler products and Eisenstein series on orthogonal groups
    • VI. Euler products and Eisenstein series on Clifford groups
  • Additional Material
     
     
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 1092004; 275 pp
MSC: Primary 11; 15; 22;

In this book, award-winning author Goro Shimura treats new areas and presents relevant expository material in a clear and readable style. Topics include Witt's theorem and the Hasse principle on quadratic forms, algebraic theory of Clifford algebras, spin groups, and spin representations. He also includes some basic results not readily found elsewhere.

The two principle themes are:

(1) Quadratic Diophantine equations;

(2) Euler products and Eisenstein series on orthogonal groups and Clifford groups.

The starting point of the first theme is the result of Gauss that the number of primitive representations of an integer as the sum of three squares is essentially the class number of primitive binary quadratic forms. Presented are a generalization of this fact for arbitrary quadratic forms over algebraic number fields and various applications. For the second theme, the author proves the existence of the meromorphic continuation of a Euler product associated with a Hecke eigenform on a Clifford or an orthogonal group. The same is done for an Eisenstein series on such a group.

Beyond familiarity with algebraic number theory, the book is mostly self-contained. Several standard facts are stated with references for detailed proofs.

Goro Shimura won the 1996 Steele Prize for Lifetime Achievement for “his important and extensive work on arithmetical geometry and automorphic forms”.

Readership

Graduate students and research mathematicians interested in number theory and algebraic groups.

  • Chapters
  • I. Algebraic theory of quadratic forms, Clifford algebras, and spin groups
  • II. Quadratic forms, Clifford algebras, and spin groups over a local or global field
  • III. Quadratic Diophantine equations
  • IV. Groups and symmetric spaces over R
  • V. Euler products and Eisenstein series on orthogonal groups
  • VI. Euler products and Eisenstein series on Clifford groups
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.