Xinyi Yuan & Shou-wu Zhang 
The Gross-Zagier Formula on Shimura Curves [EPUB ebook] 
(AMS-184)

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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.

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Über den Autor

Xinyi Yuan is assistant professor of mathematics at Princeton University.
Shou-wu Zhang is professor of mathematics at Princeton University and Columbia University.
Wei Zhang is assistant professor of mathematics at Columbia University.

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Sprache Englisch ● Format EPUB ● Seiten 272 ● ISBN 9781400845644 ● Dateigröße 37.5 MB ● Verlag Princeton University Press ● Ort Princeton ● Land US ● Erscheinungsjahr 2012 ● herunterladbar 24 Monate ● Währung EUR ● ID 6481655 ● Kopierschutz Adobe DRM
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