04013nam 2200781Ia 450 991045333130332120200520144314.097866138839191-4008-4564-51-283-57146-310.1515/9781400845644(CKB)2550000001253011(EBL)999948(OCoLC)808673192(SSID)ssj0000711359(PQKBManifestationID)11439663(PQKBTitleCode)TC0000711359(PQKBWorkID)10681688(PQKB)10318931(MiAaPQ)EBC999948(StDuBDS)EDZ0000407016(DE-B1597)447301(OCoLC)979881796(DE-B1597)9781400845644(PPN)199244790sudoc(PPN)177052295(Au-PeEL)EBL999948(CaPaEBR)ebr10590916(CaONFJC)MIL388391(EXLCZ)99255000000125301120120424h20122013 uy 0engur|n|---|||||txtccrThe Gross-Zagier formula on Shimura curves[electronic resource] /Xinyi Yuan, Shou-wu Zhang, and Wei ZhangCourse BookPrinceton Princeton University Press2012, c20131 online resource (267 p.)Annals of mathematics studies ;no. 184Description based upon print version of record.0-691-15592-5 0-691-15591-7 Includes bibliographical references and index. Frontmatter -- Contents -- Preface -- Chapter One. Introduction and Statement of Main Results -- Chapter Two. Weil Representation and Waldspurger Formula -- Chapter Three. Mordell-Weil Groups and Generating Series -- Chapter Four. Trace of the Generating Series -- Chapter Five. Assumptions on the Schwartz Function -- Chapter Six. Derivative of the Analytic Kernel -- Chapter Seven. Decomposition of the Geometric Kernel -- Chapter Eight. Local Heights of CM Points -- Bibliography -- IndexThis 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.Annals of Mathematics StudiesShimura varietiesArithmetical algebraic geometryAutomorphic formsQuaternionsElectronic books.Shimura varieties.Arithmetical algebraic geometry.Automorphic forms.Quaternions.516.3/52Yuan Xinyi1981-521265Zhang Shouwu1053006Zhang Wei1981-1053007MiAaPQMiAaPQMiAaPQBOOK9910453331303321The Gross-Zagier formula on Shimura curves2484633UNINA01314nam 2200397 450 991016491210332120230808195352.01-61312-957-2(CKB)3710000000856661(MiAaPQ)EBC4678513(EXLCZ)99371000000085666120180911d2016 uy 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierThe 24-hour wine expert /Jancis RobinsonNew York :Abrams Image,2016.1 online resource (112 pages) illustrations"Red, white, rosé, fizzy, screwcap v cork, wine myths, overpriced wines, matching food and wine, decanting, the tasting ritual, by the most respected wine critic in the world"--Cover.1-4197-2266-2 Includes bibliographical references (page 112).Wine and wine makingPopular worksWine districtsPopular worksWine and wine makingWine districts641.2/2Robinson Jancis89496MiAaPQMiAaPQMiAaPQBOOK9910164912103321The 24-hour wine expert2886558UNINA