TY  - BOOK
AU  - Yuan,Xinyi
AU  - Zhang,Shouwu
AU  - Zhang,Wei
TI  - The Gross-Zagier formula on Shimura curves
T2  - Annals of mathematics studies
SN  - 9781400845644
AV  - QA242.5 .Y83 2012eb
U1  - 516.3/52 23
PY  - 2012///, ©2013
CY  - Princeton
PB  - Princeton University Press
KW  - Shimura varieties
KW  - Arithmetical algebraic geometry
KW  - Automorphic forms
KW  - Quaternions
KW  - Variétés de Shimura
KW  - Géométrie algébrique arithmétique
KW  - Formes automorphes
KW  - MATHEMATICS
KW  - Geometry
KW  - Algebraic
KW  - bisacsh
KW  - fast
KW  - Electronic books
N1  - 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 --; Index
N2  - 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
UR  - https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=479005
ER  -