Notes on gross-zagier formula pdf
WebWith this setup, Gross and Zagier proved: Theorem: L ′ ( E / K, 1) = h ^ ( y K) ∬ E ( C) ω ∧ i ω D, where ω is the invariant differential on E (suitably normalized), and D is the discriminant … http://math.columbia.edu/~goldfeld/GaussProblem.pdf
Notes on gross-zagier formula pdf
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http://davidrenshawhansen.com/gztalk.pdf WebGross{Zagier formula is: (1) L0(E=K;1) = (easy stu ) (period) bh(y): Here the \easy stu " is made up of things like the degree of ˇ, the number of units of O K, etc.; it’s always non …
Webfollowing Zagier’s computations, we will instead consider the curve 61.a1 and do all the computations from scratch. The notes are structured around the computation of this … WebHistory: Gross-Zagier formula A: an elliptic curve over Q: A(Q): nitely generated abelian group. Birch and Swinnerton-Dyer conjecture: rank ZA(Q) = ord s=1L(A;s): Question: If …
WebGross-Zagier formula computes L!(1,E /K) as the value of a height function. Given a finite extension k/Q,letM k be the set of all places ofk and let · v be the corresponding … 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 ...
Webization [Dag] of Gross’ formula for special values of L-series [Gr1]. Theorem A can be viewed as a p-adic analytic analogue of the Gross-Zagier formula, and was sug-gested by the conjectures of Mazur-Tate-Teitelbaum type formulated in [BD1], ch. 5. It is considerably simpler to prove than the Gross-Zagier formula, as it involves
WebWe 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 … how many americans use acupunctureWeb4 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 … how many americans use the internetWebSep 1, 2024 · The original proof of (1.3) given by Gross and Zagier [12] relies on deep connections between the modular -invariant and elliptic curves. In recent work [21], the author of the present work... how many americans use weedWebThe 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, … how many americans use tiktok dailyWebCUBE SUM PROBLEM AND AN EXPLICIT GROSS-ZAGIER FORMULA LI CAI, JIE SHU, AND YE TIAN Contents 1. Introduction and Main Results 1 2. Nontriviality of Heegner Points 6 3. An Explicit Gross-Zagier Formula 12 ... Note that the torsion part of the Mordell-Weil group C(n)(Q) is trivial unless 2n is a cube, which is not a cube sum high outburst roadWebTélécharger comme PDF; Version imprimable Wei Zhang. Biographie; Naissance: 18 juillet 1981 (41 ... en plus de Borcherds, sur les travaux de Hirzebruch et Zagier [2], ainsi que ceux de Zagier/Gross/Kohnen (1986/1987). Ses collaborations avec Zhiwei Yun, ... « On p-adic Waldspurger formula ». Notes et références (en) Cet article est ... high out bursaWebon Gross{Zagier formula ([YZZ]) which serves as a prototype of the more gen-eral arithmetic restriction problems (stated in e.g., [Zh4]). We then present the relative trace formula … how many americans volunteer