The Leading eBooks Store Online 3,788,875 members ⚫ 1,234,658 ebooks

New to

Learn more

The Gross-Zagier Formula on Shimura Curves

The Gross-Zagier Formula on Shimura Curves by Xinyi Yuan
Add to cart
US$ 87.50 US$ 79.63
(If any tax is payable it will be calculated and shown at checkout.)

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.

Princeton University Press; November 2012
272 pages; ISBN 9781400845644
Read online, or download in secure EPUB or secure PDF format
Title: The Gross-Zagier Formula on Shimura Curves
Author: Xinyi Yuan; Shou-wu Zhang; Wei Zhang