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$p$-adic $L$-Functions and $p$-adic Representations
 
Bernadette Perrin-Riou Université Paris Sud, Paris, France
A co-publication of the AMS and the Société Mathématique de France
p-adic L-Functions and p-adic Representations
Softcover ISBN:  978-0-8218-1946-3
Product Code:  SMFAMS/3
List Price: $68.00
MAA Member Price: $61.20
AMS Member Price: $54.40
p-adic L-Functions and p-adic Representations
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$p$-adic $L$-Functions and $p$-adic Representations
Bernadette Perrin-Riou Université Paris Sud, Paris, France
A co-publication of the AMS and the Société Mathématique de France
Softcover ISBN:  978-0-8218-1946-3
Product Code:  SMFAMS/3
List Price: $68.00
MAA Member Price: $61.20
AMS Member Price: $54.40
  • Book Details
     
     
    SMF/AMS Texts and Monographs
    Volume: 32000; 150 pp
    MSC: Primary 11;

    Traditionally, \(p\)-adic \(L\)-functions have been constructed from complex \(L\)-functions via special values and Iwasawa theory. In this volume, Perrin-Riou presents a theory of \(p\)-adic \(L\)-functions coming directly from \(p\)-adic Galois representations (or, more generally, from motives). This theory encompasses, in particular, a construction of the module of \(p\)-adic \(L\)-functions via the arithmetic theory and a conjectural definition of the \(p\)-adic \(L\)-function via its special values.

    Since the original publication of this book in French (see Astérisque 229, 1995), the field has undergone significant progress. These advances are noted in this English edition. Also, some minor improvements have been made to the text.

    Titles in this series are co-published with Société Mathématique de France. SMF members are entitled to AMS member discounts.

    Readership

    Graduate students and research mathematicians interested in number theory.

  • Table of Contents
     
     
    • Cover
    • Series page
    • Title page
    • Copyright
    • Contents
    • Preface
    • Addendum
    • Notation
    • 1. Construction of the module of $p$-adic $L$-functions without factors at infinity
    • 2. Modules of $p$-adic $L$-functions of $V$
    • 3. Values of the module of $p$-adic $L$-functions
    • 4. The $p$-adic $L$-function of a motive
    • Appendix A. Results in Galois cohomology
    • Appendix B. The weak Leopoldt conjecture
    • Appendix C. Local Tamagawa numbers and Euler-Poincare characteristic. Application to the functional equation.
    • Bibliography
    • Index
    • Back Cover
  • Additional Material
     
     
  • Reviews
     
     
    • Written in a concise but readable style and can be recommended to readers interested in this rapidly growing subject.

      European Mathematical Society Newsletter
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 32000; 150 pp
MSC: Primary 11;

Traditionally, \(p\)-adic \(L\)-functions have been constructed from complex \(L\)-functions via special values and Iwasawa theory. In this volume, Perrin-Riou presents a theory of \(p\)-adic \(L\)-functions coming directly from \(p\)-adic Galois representations (or, more generally, from motives). This theory encompasses, in particular, a construction of the module of \(p\)-adic \(L\)-functions via the arithmetic theory and a conjectural definition of the \(p\)-adic \(L\)-function via its special values.

Since the original publication of this book in French (see Astérisque 229, 1995), the field has undergone significant progress. These advances are noted in this English edition. Also, some minor improvements have been made to the text.

Titles in this series are co-published with Société Mathématique de France. SMF members are entitled to AMS member discounts.

Readership

Graduate students and research mathematicians interested in number theory.

  • Cover
  • Series page
  • Title page
  • Copyright
  • Contents
  • Preface
  • Addendum
  • Notation
  • 1. Construction of the module of $p$-adic $L$-functions without factors at infinity
  • 2. Modules of $p$-adic $L$-functions of $V$
  • 3. Values of the module of $p$-adic $L$-functions
  • 4. The $p$-adic $L$-function of a motive
  • Appendix A. Results in Galois cohomology
  • Appendix B. The weak Leopoldt conjecture
  • Appendix C. Local Tamagawa numbers and Euler-Poincare characteristic. Application to the functional equation.
  • Bibliography
  • Index
  • Back Cover
  • Written in a concise but readable style and can be recommended to readers interested in this rapidly growing subject.

    European Mathematical Society Newsletter
Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.