The GrossZagier Formula on Shimura Curves (eBook)
by Xinyi Yuan, Shouwu Zhang, Wei Zhang (Author)

 56,301 Words
 272 Pages
This comprehensive account of the GrossZagier formula on Shimura curves over totally real fields relates the heights of Heegner points on abelian varieties to the derivatives of Lseries. The formula will have new applications for the Birch and SwinnertonDyer conjecture and Diophantine equations.
The book begins with a conceptual formulation of the GrossZagier 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 Lseries by means of Weil representations. The GrossZagier 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 GrossZagier formula is reduced to local formulas.
The GrossZagier Formula on Shimura Curves will be of great use to students wishing to enter this area and to those already working in it.
 Released: November 11, 2012
 Categories: Education
 Language: English
 Publisher: Princeton University Press
 ISBN10: 1400845645
 ISBN13: 9781400845644