| Title:
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THE GROSS-ZAGIER FORMULA ON SHIMURA CURVES
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| By: |
Xinyi Yuan, Shou-Wu Zhang, Wei Zhang |
| Format: |
Paperback |
| List price:
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£92.00 |
| Our price: |
£73.60 |
| Discount: |
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| You save:
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£18.40 |
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| ISBN 10: |
0691155925 |
| ISBN 13: |
9780691155920 |
| Availability: |
Usually dispatched within 1-3 weeks.
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| Stock: |
Currently 0 available |
| Publisher: |
PRINCETON UNIVERSITY PRESS |
| Pub. date: |
2 December, 2012 |
| Series: |
Annals of Mathematics Studies |
| Pages: |
272 |
| Description: |
Offers a comprehensive account of the Gross-Zagier formula on Shimura curves over real fields relates the heights of Heegner points on abelian varieties to the derivatives of L-series. This title begins with a conceptual formulation of the Gross-Zagier formula in terms of incoherent quaternion algebras and incoherent automorphic representations. |
| Synopsis: |
This comprehensive account of the Gross-Zagier formula on Shimura curves over totally real fields relates the heights of Heegner points on abelian varieties to the derivatives of L-series. The formula will have new applications for the Birch and Swinnerton-Dyer conjecture and Diophantine equations. The book begins with a conceptual formulation of the Gross-Zagier formula in terms of incoherent quaternion algebras and incoherent automorphic representations with rational coefficients attached naturally to abelian varieties parametrized by Shimura curves. This is followed by a complete proof of its coherent analogue: the Waldspurger formula, which relates the periods of integrals and the special values of L-series by means of Weil representations. The Gross-Zagier formula is then reformulated in terms of incoherent Weil representations and Kudla's generating series. Using Arakelov theory and the modularity of Kudla's generating series, the proof of the Gross-Zagier formula is reduced to local formulas. The Gross-Zagier Formula on Shimura Curves will be of great use to students wishing to enter this area and to those already working in it. |
| Publication: |
US |
| Imprint: |
Princeton University Press |
| Returns: |
Returnable |