{"product_id":"the-gross-zagier-formula-on-shimura-xinyi-yuan-9780691155920","title":"The Gross-Zagier Formula on Shimura Curves: (Ams-184)","description":"\u003cp\u003eThis 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. \u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e 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. \u003cp\u003e\u003c\/p\u003e\u003cbr\u003e \u003ci\u003eThe Gross-Zagier Formula on Shimura Curves\u003c\/i\u003e 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 0691155925\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9780691155920\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 Paperback\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 0.85lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.10h x 6.10w x 0.50d","brand":"Xinyi Yuan","offers":[{"title":"Paperback","offer_id":43946949345535,"sku":"9780691155920","price":103.0,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/products\/img_a3c0c0cb-90aa-4eca-a219-4f12ce0371e0.jpg?v=1681515866","url":"https:\/\/www.whiterainbookhouse.com\/products\/the-gross-zagier-formula-on-shimura-xinyi-yuan-9780691155920","provider":"WR Book House","version":"1.0","type":"link"}