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Heegner Points and Rankin L-Series

$64.99

Part of Mathematical Sciences Research Institute Publications

Henri Darmon, Shour-Wu Zhang, Bryan Birch, Benedict Gross, Dorian Goldfeld, Brian Conrad, W. R. Mann, Vinayak Vatsal, Stephen Kudla, Tonghai Yang, Doug Ulmer, Henri Darmon, Massimo Bertonlini, Peter Green
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  • Date Published: August 2010
  • availability: Available
  • format: Paperback
  • isbn: 9780521158206

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About the Authors
  • Based on a workshop on Special Values of Rankin L-series held at the MSRI in December 2001, this volume presents thirteen articles written by leading contributors on the history of the Gross-Zagier formula and recent developments. Topics include the theory of complex multiplication, automorphic forms, the Rankin-Selberg method, arithmetic intersection theory, and Iwasawa theory.

    • Includes historical and expository articles by some of the leading contributors in the field
    • Valuable reference for mathematicians
    • Based on a workshop on Special Values of Rankin L-series
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    Reviews & endorsements

    "The volume has an excellent array of topics and it is written by the leading mathematicians in the field. Each article serves well as an overview of the main concepts and definitely encourages the reader to pursue a deeper study of the field." MAA Reviews, Alvara Lozano-Robledo, Cornell University

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    Product details

    • Date Published: August 2010
    • format: Paperback
    • isbn: 9780521158206
    • length: 382 pages
    • dimensions: 234 x 156 x 20 mm
    • weight: 0.54kg
    • availability: Available
  • Table of Contents

    1. Preface Henri Darmon and Shour-Wu Zhang
    2. Heegner points: the beginnings Bryan Birch
    3. Correspondence Bryan Birch and Benedict Gross
    4. The Gauss class number problem for imaginary quadratic fields Dorian Goldfeld
    5. Heegner points and representation theory Brian Conrad (with an appendix by W. R. Mann)
    6. Special value formulae for Rankin L-functions Vinayak Vatsal
    7. Gross-Zagier formula for GL(2), II Shou-Wu Zhang
    8. Special cycles and derivatives in Eisenstein series Stephen Kudla
    9. Faltings' height and the Derivatives of Eisenstein series Tonghai Yang
    10. Elliptic curves and analogies between number fields and function fields Doug Ulmer
    11. Heegner points and elliptic curves of large rank over function fields Henri Darmon
    12. Periods and points attached to quadratic algebras Massimo Bertolini and Peter Green.

  • Editors

    Henri Darmon, McGill University, Montréal

    Shou-wu Zhang, Columbia University, New York

    Contributors

    Henri Darmon, Shour-Wu Zhang, Bryan Birch, Benedict Gross, Dorian Goldfeld, Brian Conrad, W. R. Mann, Vinayak Vatsal, Stephen Kudla, Tonghai Yang, Doug Ulmer, Henri Darmon, Massimo Bertonlini, Peter Green

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