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Arithmetic of $L$-functions
 
Edited by: Cristian Popescu University of California, San Diego, La Jolla, CA
Karl Rubin University of California, Irvine, Irvine, CA
Alice Silverberg University of California, Irvine, Irvine, CA
A co-publication of the AMS and IAS/Park City Mathematics Institute
Arithmetic of $L$-functions
Arithmetic of $L$-functions
Hardcover ISBN:  978-0-8218-5320-7
Product Code:  PCMS/18
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
eBook ISBN:  978-1-4704-1632-4
Product Code:  PCMS/18.E
List Price: $112.00
MAA Member Price: $100.80
AMS Member Price: $89.60
Hardcover ISBN:  978-0-8218-5320-7
eBook: ISBN:  978-1-4704-1632-4
Product Code:  PCMS/18.B
List Price: $237.00 $181.00
MAA Member Price: $213.30 $162.90
AMS Member Price: $189.60 $144.80
Arithmetic of $L$-functions
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Arithmetic of $L$-functions
Arithmetic of $L$-functions
Edited by: Cristian Popescu University of California, San Diego, La Jolla, CA
Karl Rubin University of California, Irvine, Irvine, CA
Alice Silverberg University of California, Irvine, Irvine, CA
A co-publication of the AMS and IAS/Park City Mathematics Institute
Hardcover ISBN:  978-0-8218-5320-7
Product Code:  PCMS/18
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
eBook ISBN:  978-1-4704-1632-4
Product Code:  PCMS/18.E
List Price: $112.00
MAA Member Price: $100.80
AMS Member Price: $89.60
Hardcover ISBN:  978-0-8218-5320-7
eBook ISBN:  978-1-4704-1632-4
Product Code:  PCMS/18.B
List Price: $237.00 $181.00
MAA Member Price: $213.30 $162.90
AMS Member Price: $189.60 $144.80
  • Book Details
     
     
    IAS/Park City Mathematics Series
    Volume: 182011; 499 pp
    MSC: Primary 11; 14;

    The overall theme of the 2009 IAS/PCMI Graduate Summer School was connections between special values of \(L\)-functions and arithmetic, especially the Birch and Swinnerton-Dyer Conjecture and Stark's Conjecture. These conjectures are introduced and discussed in depth, and progress made over the last 30 years is described. This volume contains the written versions of the graduate courses delivered at the summer school. It would be a suitable text for advanced graduate topics courses on the Birch and Swinnerton-Dyer Conjecture and/or Stark's Conjecture. The book will also serve as a reference volume for experts in the field.

    Readership

    Graduate students and research mathematicians interested in number theory and \(L\)-functions.

  • Table of Contents
     
     
    • Chapters
    • Introduction
    • Part I. Stark’s conjecture
    • Stark’s basic conjecture
    • The origin of the “Stark conjectures”
    • Integral and $p$-adic refinements of the abelian Stark conjecture
    • Special values of $L$-functions at negative integers
    • An introduction to the equivariant Tamagawa number conjecture: The relation to Stark’s conjecture
    • Part II. Birch and Swinnerton-Dyer conjecture
    • Introduction to elliptic curves
    • Lectures on the conjecture of Birch and Swinnerton-Dyer
    • Elliptic curves over function fields
    • Heegner’s proof
    • Complex multiplication: A concise introduction
    • The equivariant Tamagawa number conjecture and the Birch-Swinnerton-Dyer conjecture
    • Part III. Analytic and cohomological methods
    • Root numbers
    • Euler systems and Kolyvagin systems
  • Additional Material
     
     
  • Reviews
     
     
    • ...anyone interested in learning about the arithmetic of L-functions would be well-served by this book.

      MAA Reviews
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 182011; 499 pp
MSC: Primary 11; 14;

The overall theme of the 2009 IAS/PCMI Graduate Summer School was connections between special values of \(L\)-functions and arithmetic, especially the Birch and Swinnerton-Dyer Conjecture and Stark's Conjecture. These conjectures are introduced and discussed in depth, and progress made over the last 30 years is described. This volume contains the written versions of the graduate courses delivered at the summer school. It would be a suitable text for advanced graduate topics courses on the Birch and Swinnerton-Dyer Conjecture and/or Stark's Conjecture. The book will also serve as a reference volume for experts in the field.

Readership

Graduate students and research mathematicians interested in number theory and \(L\)-functions.

  • Chapters
  • Introduction
  • Part I. Stark’s conjecture
  • Stark’s basic conjecture
  • The origin of the “Stark conjectures”
  • Integral and $p$-adic refinements of the abelian Stark conjecture
  • Special values of $L$-functions at negative integers
  • An introduction to the equivariant Tamagawa number conjecture: The relation to Stark’s conjecture
  • Part II. Birch and Swinnerton-Dyer conjecture
  • Introduction to elliptic curves
  • Lectures on the conjecture of Birch and Swinnerton-Dyer
  • Elliptic curves over function fields
  • Heegner’s proof
  • Complex multiplication: A concise introduction
  • The equivariant Tamagawa number conjecture and the Birch-Swinnerton-Dyer conjecture
  • Part III. Analytic and cohomological methods
  • Root numbers
  • Euler systems and Kolyvagin systems
  • ...anyone interested in learning about the arithmetic of L-functions would be well-served by this book.

    MAA Reviews
Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
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