The Gross-Zagier Formula on Shimura Curves 在線電子書 pdf 下載 txt下載 epub 下載 mobi 下載 2024

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Xinyi Yuan 作者

Princeton University Press

譯者

2012-12-2 出版日期

272 頁數

GBP 149.95 價格

Hardcover

叢書系列

9780691155913 圖書編碼

The Gross-Zagier Formula on Shimura Curves 在線電子書圖書標籤: 數論數學誌村簇

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發表於2024-12-24

The Gross-Zagier Formula on Shimura Curves 在線電子書 epub 下載 mobi 下載 pdf 下載 txt 下載 2024

The Gross-Zagier Formula on Shimura Curves 在線電子書 epub 下載 pdf 下載 mobi 下載 txt 下載 2024

The Gross-Zagier Formula on Shimura Curves 在線電子書 pdf 下載 txt下載 epub 下載 mobi 下載 2024

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The Gross-Zagier Formula on Shimura Curves 在線電子書 pdf 下載 txt下載 epub 下載 mobi 在線電子書下載

The Gross-Zagier Formula on Shimura Curves 在線電子書圖書描述

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.

The Gross-Zagier Formula on Shimura Curves 在線電子書下載 mobi epub pdf txt 在線電子書下載

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