Notes on gross-zagier formula pdf
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 … 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, …
Notes on gross-zagier formula pdf
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http://math.columbia.edu/~goldfeld/GaussProblem.pdf WebCUBE 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
WebThe purpose of this paper is to discuss some work on elliptic curves over function fields inspired by the Gross–Zagier theorem and to present new ideas about ranks of elliptic curves from the function field case which I hope will inspire work over number fields. 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
Web1. AN OVERVIEW OF THE GROSS-ZAGIER AND WALDSPURGER FORMULAS (YUNQING TANG)9 The theory of complex multiplication implies that Heegner points are defined … Webon 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 …
Web0(N), Gross–Kohnen–Zagier prove [2] that certain generating series of Heegner points are modular forms of weight 3/2 with values in Jacobian as a consequence of their formula for N´eron-Tate height pairing of Heegner points. Such a result is …
http://math.columbia.edu/~goldfeld/GaussProblem.pdf schenectady movies showtimesWebHere Gross and Zagier take inspiration from Siegel, who wrote down a two-variable Hecke-Eisenstein series corresponding to K, restricted to the diagonal, and got a modular form … schenectady movieplexWebNov 20, 2024 · The theorems of Gross–Zagier and Zhang relate the Néron–Tate heights of complex ... Zhang, S.-W., Gross-Zagier formula for GL(2). II. In: Heegner Points and Rankin … ruth bergerWeb4 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 … ruth bergevin wifeWeb2 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 ... ruth bergevinWebToday we will define the objects on the two sides of the Gross–Zagier formula (one side is in terms of L-series of modular forms, the other side is in terms of Heegner points on X 0(N)). Then we can state the main theorem precisely. 1Heegner points Let x= (ϕ: E→E′) be an isogeny of elliptic curves over C, cyclic of degree N. By abuse we ruth berkley south tynesideWebWith 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 … schenectady mltc