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Record Nr. |
UNINA9910790961403321 |
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Autore |
Yuan Xinyi <1981-> |
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Titolo |
The Gross-Zagier formula on Shimura curves [[electronic resource] /] / Xinyi Yuan, Shou-wu Zhang, and Wei Zhang |
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Pubbl/distr/stampa |
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Princeton, : Princeton University Press, 2012, c2013 |
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ISBN |
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9786613883919 |
1-4008-4564-5 |
1-283-57146-3 |
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Edizione |
[Course Book] |
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Descrizione fisica |
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1 online resource (267 p.) |
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Collana |
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Annals of mathematics studies ; ; no. 184 |
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Altri autori (Persone) |
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ZhangShouwu |
ZhangWei <1981-> |
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Disciplina |
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Soggetti |
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Shimura varieties |
Arithmetical algebraic geometry |
Automorphic forms |
Quaternions |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Description based upon print version of record. |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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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 |
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Sommario/riassunto |
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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 |
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