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Heegner points and Rankin L-series /
The seminal formula of Gross and Zagier relating heights of Heegner points to derivatives of the associated Rankin L-series has led to many generalisations and extensions in a variety of different directions, spawning a fertile area of study that remains active to this day. This volume, based on a w...
| Clasificación: | Libro Electrónico |
|---|---|
| Otros Autores: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge, UK ; New York, NY, USA :
Cambridge University Press,
©2004.
|
| Colección: | Mathematical Sciences Research Institute publications ;
49. |
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 245 | 0 | 0 | |a Heegner points and Rankin L-series / |c edited by Henri Darmon, Shou-Wu Zhang. |
| 260 | |a Cambridge, UK ; |a New York, NY, USA : |b Cambridge University Press, |c ©2004. | ||
| 300 | |a 1 online resource (xiii, 367 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
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| 490 | 1 | |a Mathematical Sciences Research Institute publications ; |v 49 | |
| 504 | |a Includes bibliographical references and index. | ||
| 588 | 0 | |a Print version record. | |
| 520 | |a The seminal formula of Gross and Zagier relating heights of Heegner points to derivatives of the associated Rankin L-series has led to many generalisations and extensions in a variety of different directions, spawning a fertile area of study that remains active to this day. This volume, based on a workshop on Special Values of Rankin L-series held at the MSRI in December 2001, is a collection of thirteen articles written by many of the leading contributors in the field, having the Gross-Zagier formula and its avatars as a common unifying theme. It serves as a valuable reference for mathematicians wishing to become further acquainted with the theory of complex multiplication, automorphic forms, the Rankin-Selberg method, arithmetic intersection theory, Iwasawa theory, and other topics related to the Gross-Zagier formula. | ||
| 505 | 0 | |a Cover -- Half-title -- Series-title -- Title -- Copyright -- Contents -- Preface -- Heegner Points: The Beginnings -- 1. Prologue: The Opportune Arrival of Heegner Points -- 2. Prehistory -- 3. Heegner -- 4. Simplification and Generalisation -- 5. 1982 -- References -- Correspondence -- Gross to Birch: March 1, 1982 -- Birch to Gross: May 6, 1982 -- Gross to Birch: May 14, 1982 -- Birch to Gross: around September 6, 1982 -- Gross to Birch: September 17, 1982 -- Gross to Birch: December 1, 1982 -- Birch to Gross: December 27, 1982. | |
| 505 | 8 | |a The Gauss Class Number Problem for Imaginary Quadratic Fields -- 1. Introduction -- 2. The Deuring-Heilbronn Phenomenon -- 3. Existence of L-functions of Elliptic Curves with Triple Zeros -- 4. Solution of the Class Number One Problem -- Acknowledgment -- References -- Heegner Points and Representation Theory -- 1. Heegner Points on X0(N) -- 2. Rankin L-Series and a Height Formula -- 3. Starting from the L-Function -- 4. Local Representation Theory -- 5. Unitary Similitudes -- 6. The L-Group and Its Symplectic Representation -- 7. Inner Forms -- 8. Langlands Parameters -- 9. Local epsilon Factors. | |
| 505 | 8 | |a 10. Local Linear Forms -- 11. Local Test Vectors -- 12. An Explicit Local Formula -- 13. Ad grave accent lic Groups -- 14. A Special Case -- 15. Automorphic Representations -- 16. When #S Is Even -- 17. Global Test Vectors -- 18. An Explicit Global Formula -- 19. When #S Is Odd -- 20. Shimura Varieties -- 21. Nearby Quaternion Algebras -- 22. The Global Representation -- 23. The Global Linear Form -- 24. Global Test Vectors -- Acknowledgment -- References -- Gross-Zagier Revisited -- 1. Introduction -- 2. Some Properties of Abelian Schemes and Modular Curves. | |
| 505 | 8 | |a 3. The Serre-Tate Theorem and the Grothendieck Existence Theorem -- 4. Computing Naive Intersection Numbers -- 5. Intersection Formula Via Hom Groups -- 6. Supersingular Cases with r A(m) = 0 -- 7. Application of a Construction of Serre -- 8. Intersection Theory Via Meromorphic Tensors -- 9. Self-Intersection Formula and Application to Global Height Pairings -- 10. Quaternionic Explications -- Appendix by W.R. Mann: Elimination of Quaternionic Sums -- References -- Special Value Formulae for Rankin L-Functions -- 1. Introduction -- 2. Notation and Hypotheses -- 3. Atkin-Lehner Theory on GL2. | |
| 505 | 8 | |a 4. Quaternion Algebras and the Jacquet-Langlands Correspondence -- 5. The Work of Waldspurger -- 6. Test Vectors: The Work of Gross and Prasad -- 7. The Work of Gross and Zhang -- References -- Gross-Zagier Formula for GL(2), II -- 1. Introduction and Notation -- 2. Automorphic Forms -- 3. Weights and Levels -- 4. Automorphic L-Series -- 5. Rankin-Selberg L-Series -- 6. The Odd Case -- 7. The Even Case -- 8. The Idea of Gross and Zagier -- 9. Calculus on Arithmetic Surfaces -- 10. Decomposition of Heights -- 11. Construction of the Kernels -- 12. Geometric Pairing. | |
| 546 | |a English. | ||
| 590 | |a ProQuest Ebook Central |b Ebook Central Academic Complete | ||
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| 650 | 0 | |a Curves, Elliptic. | |
| 650 | 0 | |a L-functions. | |
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| 650 | 6 | |a Fonctions L. | |
| 650 | 7 | |a MATHEMATICS |x Geometry |x Algebraic. |2 bisacsh | |
| 650 | 7 | |a Curves, Elliptic |2 fast | |
| 650 | 7 | |a L-functions |2 fast | |
| 700 | 1 | |a Darmon, Henri, |d 1965- |1 https://id.oclc.org/worldcat/entity/E39PBJxrVWpf7XkTc8YhC3Tyh3 | |
| 700 | 1 | |a Zhang, Shouwu. | |
| 758 | |i has work: |a Heegner points and Rankin L-series (Text) |1 https://id.oclc.org/worldcat/entity/E39PCGHddGjhMpYhywdjdTV9WC |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 0 | 8 | |i Print version: |t Heegner points and Rankin L-series. |d Cambridge, UK ; New York, NY, USA : Cambridge University Press, ©2004 |w (DLC) 2004045108 |
| 830 | 0 | |a Mathematical Sciences Research Institute publications ; |v 49. | |
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