The Gross-Zagier formula on Shimura curves
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The work The Gross-Zagier formula on Shimura curves represents a distinct intellectual or artistic creation found in Bowdoin College Library. This resource is a combination of several types including: Work, Language Material, Books.
The Resource
The Gross-Zagier formula on Shimura curves
Resource Information
The work The Gross-Zagier formula on Shimura curves represents a distinct intellectual or artistic creation found in Bowdoin College Library. This resource is a combination of several types including: Work, Language Material, Books.
- Label
- The Gross-Zagier formula on Shimura curves
- Statement of responsibility
- Xinyi Yuan, Shou-wu Zhang, and Wei Zhang
- Language
- eng
- Summary
- "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."--Publisher's website
- Cataloging source
- DLC
- Index
- index present
- Literary form
- non fiction
- Nature of contents
- bibliography
- Series statement
- Annals of mathematics studies
- Series volume
- no. 184
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