{"product_id":"the-gross-zagier-formula-on-shimura-curves-paperback","title":"The Gross-Zagier Formula on Shimura Curves - Paperback","description":"\u003cdiv\u003e\u003cp style=\"text-align: right;\"\u003e\u003ca href=\"https:\/\/reportcopyrightinfringement.com\/\" target=\"_blank\" rel=\"nofollow\"\u003e\u003cb\u003eReport copyright infringement\u003c\/b\u003e\u003c\/a\u003e\u003c\/p\u003e\u003c\/div\u003e\u003cp\u003eby \u003cb\u003eXinyi Yuan\u003c\/b\u003e (Author), \u003cb\u003eShou-Wu Zhang\u003c\/b\u003e (Author), \u003cb\u003eWei Zhang\u003c\/b\u003e (Author)\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\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.\u003ch3\u003eAuthor Biography\u003c\/h3\u003e\u003cp\u003e\u003cb\u003eXinyi Yuan\u003c\/b\u003e is assistant professor of mathematics at Princeton University. \u003cb\u003eShou-wu Zhang\u003c\/b\u003e is professor of mathematics at Princeton University and Columbia University. \u003cb\u003eWei Zhang\u003c\/b\u003e is assistant professor of mathematics at Columbia University.\u003c\/p\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eNumber of Pages:\u003c\/strong\u003e 272\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eDimensions:\u003c\/strong\u003e 0.5 x 9.1 x 6.1 IN\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003ePublication Date:\u003c\/strong\u003e December 02, 2012\u003c\/div\u003e\n            ","brand":"BooksCloud","offers":[{"title":"Default Title","offer_id":47336838070521,"sku":"9780691155920","price":196.65,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0789\/2782\/3097\/files\/YXoybFhpLzFwenRhMzJ0YkpUWGF3dz09.webp?v=1769671372","url":"https:\/\/bookscloud.io\/products\/the-gross-zagier-formula-on-shimura-curves-paperback","provider":"BooksCloud Book Dropshipping","version":"1.0","type":"link"}