The Resource The GrossZagier formula on Shimura curves, Xinyi Yuan, Shouwu Zhang, and Wei Zhang
The GrossZagier formula on Shimura curves, Xinyi Yuan, Shouwu Zhang, and Wei Zhang
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The item The GrossZagier formula on Shimura curves, Xinyi Yuan, Shouwu Zhang, and Wei Zhang represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Bowdoin College Library.This item is available to borrow from 1 library branch.
Resource Information
The item The GrossZagier formula on Shimura curves, Xinyi Yuan, Shouwu Zhang, and Wei Zhang represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Bowdoin College Library.
This item is available to borrow from 1 library branch.
 Summary
 "This comprehensive account of the GrossZagier formula on Shimura curves over totally real fields relates the heights of Heegner points on abelian varieties to the derivatives of Lseries. The formula will have new applications for the Birch and SwinnertonDyer conjecture and Diophantine equations. The book begins with a conceptual formulation of the GrossZagier 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 Lseries by means of Weil representations. The GrossZagier 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 GrossZagier formula is reduced to local formulas. The GrossZagier Formula on Shimura Curves will be of great use to students wishing to enter this area and to those already working in it."Publisher's website
 Language
 eng
 Extent
 viii, 256 pages
 Contents

 Introduction and Statement of Main Results
 Weil Representation and Waldspurger Formula
 MordellWeil Groups and Generating Series
 Trace of the Generating Series
 Assumptions on the Schwartz Function
 Derivative of the Analytic Kernel
 Decomposition of the Geometric Kernel
 Local Heights of CM Points
 Isbn
 9780691155913
 Label
 The GrossZagier formula on Shimura curves
 Title
 The GrossZagier formula on Shimura curves
 Statement of responsibility
 Xinyi Yuan, Shouwu Zhang, and Wei Zhang
 Language
 eng
 Summary
 "This comprehensive account of the GrossZagier formula on Shimura curves over totally real fields relates the heights of Heegner points on abelian varieties to the derivatives of Lseries. The formula will have new applications for the Birch and SwinnertonDyer conjecture and Diophantine equations. The book begins with a conceptual formulation of the GrossZagier 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 Lseries by means of Weil representations. The GrossZagier 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 GrossZagier formula is reduced to local formulas. The GrossZagier Formula on Shimura Curves will be of great use to students wishing to enter this area and to those already working in it."Publisher's website
 Cataloging source
 DLC
 http://library.link/vocab/creatorDate
 1981
 http://library.link/vocab/creatorName
 Yuan, Xinyi
 Index
 index present
 Literary form
 non fiction
 Nature of contents
 bibliography
 http://library.link/vocab/relatedWorkOrContributorDate
 1981
 http://library.link/vocab/relatedWorkOrContributorName

 Zhang, Shouwu
 Zhang, Wei
 Series statement
 Annals of mathematics studies
 Series volume
 no. 184
 http://library.link/vocab/subjectName

 Shimura varieties
 Arithmetical algebraic geometry
 Automorphic forms
 Quaternions
 Label
 The GrossZagier formula on Shimura curves, Xinyi Yuan, Shouwu Zhang, and Wei Zhang
 Bibliography note
 Includes bibliographical references and index
 Carrier category
 volume
 Carrier category code

 nc
 Carrier MARC source
 rdacarrier
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents
 Introduction and Statement of Main Results  Weil Representation and Waldspurger Formula  MordellWeil Groups and Generating Series  Trace of the Generating Series  Assumptions on the Schwartz Function  Derivative of the Analytic Kernel  Decomposition of the Geometric Kernel  Local Heights of CM Points
 Control code
 791488485
 Dimensions
 24 cm
 Extent
 viii, 256 pages
 Isbn
 9780691155913
 Isbn Type
 (hardcover : alk. paper)
 Lccn
 2012010981
 Media category
 unmediated
 Media MARC source
 rdamedia
 Media type code

 n
 Label
 The GrossZagier formula on Shimura curves, Xinyi Yuan, Shouwu Zhang, and Wei Zhang
 Bibliography note
 Includes bibliographical references and index
 Carrier category
 volume
 Carrier category code

 nc
 Carrier MARC source
 rdacarrier
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents
 Introduction and Statement of Main Results  Weil Representation and Waldspurger Formula  MordellWeil Groups and Generating Series  Trace of the Generating Series  Assumptions on the Schwartz Function  Derivative of the Analytic Kernel  Decomposition of the Geometric Kernel  Local Heights of CM Points
 Control code
 791488485
 Dimensions
 24 cm
 Extent
 viii, 256 pages
 Isbn
 9780691155913
 Isbn Type
 (hardcover : alk. paper)
 Lccn
 2012010981
 Media category
 unmediated
 Media MARC source
 rdamedia
 Media type code

 n
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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.bowdoin.edu/portal/TheGrossZagierformulaonShimuracurvesXinyi/B1WXsHiANEQ/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.bowdoin.edu/portal/TheGrossZagierformulaonShimuracurvesXinyi/B1WXsHiANEQ/">The GrossZagier formula on Shimura curves, Xinyi Yuan, Shouwu Zhang, and Wei Zhang</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.bowdoin.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="https://link.bowdoin.edu/">Bowdoin College Library</a></span></span></span></span></div>