http://www.mi.uni-koeln.de/%7Ewoodbury/research/GZ-classnotes.pdf Web2 Gross-Zagier Subgroups In this section, we x our notation and conventions, and de ne the Manin constant. Then we recall the statement of the full Birch and Swinnerton-Dyer conjecture over an imaginary quadratic eld K. We give a new de nition of Gross-Zagier subgroups of E(K) and prove that they all satisfy a Gross-Zagier style formula. When r ...
Twisted Gross–Zagier Theorems - Cambridge Core
Webthe methods of Gross and Zagier and give a computable formula for v ‘(J(d 1;d 2)) for any pair of discriminants d 1 6= d 2 and any prime ‘ > 2. In the case that d 1 is squarefree and d 2 is the discriminant of any quadratic imaginary order, our formula can be stated in a simple closed form. We also give a conjectural closed formula when the ... WebThe Gross–Zagier formula Vijay Srinivasan July 27, 2024 Contents 1Modular curves I 1.1The curves Y ... We note a few properties of this definition. LetC n denote a N´eron n-gon. First, … modernships官网入口
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WebJun 21, 2005 · A new proof of Howard’s Λ-adic Gross–Zagier formula is given, via Iwasawa theory, based on the connection between Heegner points, Beilinson–Flach elements, and their explicit reciprocity laws, to the context of indefinite Shimura curves over Q attached to nonsplit quaternion algebras. 32 PDF View 2 excerpts, cites background and methods ... 1 … WebThe aim of this note is to give a survey on recent development of the Gross-Zagier formulas and their applications. The formulas relate the central derivatives (or central values) of … Web4 DORIANGOLDFELD d,a fundamental discriminant of an imaginary quadratic field.We shall need the Gross–Zagier formula (see [G–Z]) (3.1) d ds L E(s)L E(s,χ d) s=1 = c E P d,P d , where P d,P d is the height pairing of a certain Heegner point P D and c E is an explicit constant depending on the elliptic curve E.Gross and Zagier showed that if Eis an elliptic … insee transport maritime