Xinyi Yuan: The Gross-Zagier Formula on Shimura Curves, Kartoniert / Broschiert
The Gross-Zagier Formula on Shimura Curves
Buch
- Publisher:
- Princeton University Press, 12/2012
- Binding:
- Kartoniert / Broschiert, Paperback
- Language:
- Englisch
- ISBN-13:
- 9780691155920
- Item number:
- 10155094
- Volume:
- 268 Pages
- Weight:
- 388 g
- Format:
- 233 x 154 mm
- Thickness:
- 17 mm
- Release date:
- 2.12.2012
- Note
-
Caution: Product is not in German language
Blurb
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.
Biography (Wei Zhang)
Wei Zhang wurde während der Kulturrevolution in Chongqing, VR China, geboren. Sie studierte dort Anglistik. Seit 1990 lebt sie in der Schweiz. 2007 erschien ihr Buch »Zwischen den Stühlen: Geschichten von Chinesinnen und Chinesen in der Schweiz« im Verlag NZZ Libro. »Eine Mango für Mao« ist ihr erster Roman. Sie schreibt für das Feuilleton der NZZ, arbeitet daneben als Hochschuldozentin und gibt Kurse zu interkulturellen Themen.
Xinyi Yuan, Shou-Wu Zhang, Wei Zhang
The Gross-Zagier Formula on Shimura Curves
Current price: EUR 107.35