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The Gross-Zagier Formula on Shimura Curves - (AMS-184) (Paperback, New) Loot Price: R2,245
Discovery Miles 22 450
The Gross-Zagier Formula on Shimura Curves - (AMS-184) (Paperback, New): Xinyi Yuan, Shouwu Zhang, Wei Zhang

The Gross-Zagier Formula on Shimura Curves - (AMS-184) (Paperback, New)

Xinyi Yuan, Shouwu Zhang, Wei Zhang

Series: Annals of Mathematics Studies

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Loot Price R2,245 Discovery Miles 22 450 | Repayment Terms: R210 pm x 12*

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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 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.

General

Imprint: Princeton University Press
Country of origin: United States
Series: Annals of Mathematics Studies
Release date: December 2012
First published: 2013
Authors: Xinyi Yuan • Shouwu Zhang • Wei Zhang
Dimensions: 235 x 152 x 13mm (L x W x T)
Format: Paperback - Trade
Pages: 272
Edition: New
ISBN-13: 978-0-691-15592-0
Categories: Books > Science & Mathematics > Mathematics > Geometry > Algebraic geometry
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LSN: 0-691-15592-5
Barcode: 9780691155920

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