The Resource The Gross-Zagier formula on Shimura curves, Xinyi Yuan, Shou-wu Zhang, and Wei Zhang
The Gross-Zagier formula on Shimura curves, Xinyi Yuan, Shou-wu Zhang, and Wei Zhang
Resource Information
The item The Gross-Zagier formula on Shimura curves, Xinyi Yuan, Shou-wu 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 Gross-Zagier formula on Shimura curves, Xinyi Yuan, Shou-wu 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 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."--Publisher's website
- Language
- eng
- Extent
- viii, 256 pages
- Contents
-
- Introduction and Statement of Main Results
- Weil Representation and Waldspurger Formula
- Mordell-Weil 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 Gross-Zagier formula on Shimura curves
- Title
- The Gross-Zagier formula on Shimura curves
- Statement of responsibility
- Xinyi Yuan, Shou-wu Zhang, and Wei Zhang
- Language
- eng
- Summary
- "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 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."--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 Gross-Zagier formula on Shimura curves, Xinyi Yuan, Shou-wu 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 -- Mordell-Weil 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 Gross-Zagier formula on Shimura curves, Xinyi Yuan, Shou-wu 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 -- Mordell-Weil 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 fa-external-link-square fa-fw"></i> Data from <span resource="http://link.bowdoin.edu/portal/The-Gross-Zagier-formula-on-Shimura-curves-Xinyi/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/The-Gross-Zagier-formula-on-Shimura-curves-Xinyi/B1WXsHiANEQ/">The Gross-Zagier formula on Shimura curves, Xinyi Yuan, Shou-wu 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>
