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The book delves into the Gross-Zagier formula concerning Shimura curves over totally real fields, exploring the relationship between the heights of Heegner points on abelian varieties and L-series derivatives. It highlights new applications of this formula, particularly in the context of the Birch and Swinnerton-Dyer conjecture and Diophantine equations, making it a significant contribution to the field of number theory.
Buchkauf
The Gross-Zagier Formula on Shimura Curves, Xinyi Yuan, Shou-Wu Zhang, Wei Zhang
- Sprache
- Erscheinungsdatum
- 2012
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- Titel
- The Gross-Zagier Formula on Shimura Curves
- Untertitel
- (Ams-184)
- Sprache
- Englisch
- Autor*innen
- Xinyi Yuan, Shou-Wu Zhang, Wei Zhang
- Verlag
- 2012
- Einband
- Hardcover
- Seitenzahl
- 272
- ISBN13
- 9780691155913
- Kategorie
- Mathematik
- Beschreibung
- The book delves into the Gross-Zagier formula concerning Shimura curves over totally real fields, exploring the relationship between the heights of Heegner points on abelian varieties and L-series derivatives. It highlights new applications of this formula, particularly in the context of the Birch and Swinnerton-Dyer conjecture and Diophantine equations, making it a significant contribution to the field of number theory.