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[null,"1.","Record Nr.",null,"UNINA9910917986203321"]
[null,null,"Titolo",null,"Allgemeiner Jahres-Bericht / Central-Commission für die Rhein-Schiffahrt"]
[null,null,"Pubbl/distr/stampa",null,"Schneider"]
[null,null,"Lingua di pubblicazione",null,"Inglese"]
[null,null,"Formato",null,"Materiale a stampa"]
[null,null,null,"Livello bibliografico","Periodico"]
[null,"2.","Record Nr.",null,"UNINA9910962673203321"]
[null,null,"Autore",null,"Yuan Xinyi <1981->"]
[null,null,"Titolo",null,"The Gross-Zagier formula on Shimura curves / / Xinyi Yuan, Shou-wu Zhang, and Wei Zhang"]
[null,null,"Pubbl/distr/stampa",null,"Princeton, : Princeton University Press, 2012, c2013"]
[null,null,"ISBN",null,"9786613883919"]
[{"$nulls":4},"9781400845644"]
[{"$nulls":4},"1400845645"]
[{"$nulls":4},"9781283571463"]
[{"$nulls":4},"1283571463"]
[null,null,"Edizione",null,"[Course Book]"]
[null,null,"Descrizione fisica",null,"1 online resource (267 p.)"]
[null,null,"Collana",null,"Annals of mathematics studies ; ; no. 184"]
[null,null,"Disciplina",null,"516.3/52"]
[null,null,"Soggetti",null,"Shimura varieties"]
[{"$nulls":4},"Arithmetical algebraic geometry"]
[{"$nulls":4},"Automorphic forms"]
[{"$nulls":4},"Quaternions"]
[null,null,"Lingua di pubblicazione",null,"Inglese"]
[null,null,"Formato",null,"Materiale a stampa"]
[null,null,null,"Livello bibliografico","Monografia"]
[null,null,null,"Note generali","Description based upon print version of record."]
[null,null,null,"Nota di bibliografia","Includes bibliographical references and index."]
[null,null,"Nota di contenuto",null,"Frontmatter -- Contents -- Preface -- Chapter One. Introduction and Statement of Main Results -- Chapter Two. Weil Representation and Waldspurger Formula -- Chapter Three. Mordell-Weil Groups and Generating Series -- Chapter Four. Trace of the Generating Series -- Chapter Five. Assumptions on the Schwartz Function -- Chapter Six. Derivative of the Analytic Kernel -- Chapter Seven. Decomposition of the Geometric Kernel -- Chapter Eight. Local Heights of CM Points -- Bibliography -- Index"]
[null,null,null,"Sommario/riassunto","This comprehensive account of the Gross-Zagier formula on Shimura curves over totally real fields relates the heights of Heegner points on abelian varieties to the derivatives of L-series. The formula will have new applications for the Birch and Swinnerton-Dyer conjecture and Diophantine equations. The book begins with a conceptual formulation of the Gross-Zagier formula in terms of incoherent quaternion algebras and incoherent automorphic representations with rational coefficients attached naturally to abelian varieties parametrized by Shimura curves. This is followed by a complete proof of its coherent analogue: the Waldspurger formula, which relates the periods of integrals and the "]
[{"$nulls":4},"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."]