{"product_id":"the-gross-zagier-formula-on-shimura-xinyi-yuan-9780691155913","title":"The Gross-Zagier Formula on Shimura Curves: (Ams-184)","description":"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.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e Xinyi Yuan, Shou-Wu Zhang, Wei Zhang\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 0691155917\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9780691155913\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Princeton University Press\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 12\/02\/2012\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 272\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Hardcover\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 1.22lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.21h x 6.14w x 0.63d","brand":"Xinyi Yuan","offers":[{"title":"Hardcover","offer_id":44254732386559,"sku":"9780691155913","price":200.0,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/files\/img_bbf3b95a-f5ca-4a1d-9aef-883b967809e2.jpg?v=1694614057","url":"https:\/\/www.whiterainbookhouse.com\/products\/the-gross-zagier-formula-on-shimura-xinyi-yuan-9780691155913","provider":"WR Book House","version":"1.0","type":"link"}