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OverviewThis 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. Full Product DetailsAuthor: Xinyi Yuan , Shou-wu Zhang , Wei ZhangPublisher: Princeton University Press Imprint: Princeton University Press Volume: 208 Weight: 0.510kg ISBN: 9780691155913ISBN 10: 0691155917 Pages: 272 Publication Date: 02 December 2012 Audience: College/higher education , Professional and scholarly , Tertiary & Higher Education , Professional & Vocational Format: Hardback Publisher's Status: Active Availability: Manufactured on demand We will order this item for you from a manufactured on demand supplier. Language: English Table of ContentsReviewsAuthor InformationXinyi Yuan is assistant professor of mathematics at Princeton University. Shou-wu Zhang is professor of mathematics at Princeton University and Columbia University. Wei Zhang is assistant professor of mathematics at Columbia University. Tab Content 6Author Website:Countries AvailableAll regions |