Notes on gross-zagier formula pdf

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August undefined, 2024

WebSep 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... WebThe goal of the Gross-Zagier formula is to express L0(1;E=K) in terms of these previously de ned height functions. 5 The Gross-Zagier Formula and Applications Theorem 5.1. With all …

[PDF] The Iwasawa theoretic Gross–Zagier theorem - Semantic …

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 … the printery foundation

p-ADIC GROSS{ZAGIER FORMULA AT CRITICAL SLOPE AND A …

WebIn this notes, we are trying to give an intersection formula of local heights for nonarchimedean places. It closely follows ﬁrst six sections of part III in Gross-Zagier[3]. If there is any mistake in this notes, it is due to the author’s limited ... Gross-Zagierrevisited. InHeegner points and Rankin L-series, volume49ofMath. Sci. Res. Inst ... 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 … 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, … the printery cards

Gross–Zagier Formula for GL(2), II - Mathematical Sciences …

Birch’s story. Theorem 1 Some history. - Universität zu Köln

WebHere 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 … WebSuch a non-critical slope result is precisely Theorem 5.1.1 (p-adic Gross-Zagier formula for non-ordinary eigenforms of arbitrary weight; which is work in progress by Kobayashi [Kob19]). More precisely, Kobayashi’s method only establishes a p-adic Gross{Zagier formula in the non-ordinary case for one of the two p-stabilization sigma news latestWeb1.1. Introduction. The Gross-Zagier formula and the Waldspurger formula are probably the two most important analytic tools known at present for studying the still largely unproven … sigma news live

"Webfor the entire study is a p-adic formula of Gross-Zagier type which relates the images of these diagonal cycles under the p-adic Abel-Jacobi map to special values of certain p-adic L-functions attached to the Garrett-Rankintriple convolution of three Hida families of modular forms. The main goal of this article is to describe and prove this ... " - Notes on gross-zagier formula pdf

Notes on gross-zagier formula pdf

The Gross-Zagier Formula on Shimura Curves on JSTOR

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 … WebMay 11, 2016 · The Gross-Zagier formula gives something on the BSD conjecture for elliptic curves over Q. In particular the something that interest me is that if an elliptic curve as analytic rank 1, then the elliptic curve as a point of infinite order so …

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WebThis 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 … WebThis comprehensive account of the Gross-Zagier formula on Shimura curves over totally real fields relates the heights of Heegner points on abelian varieties to ...

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 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.

WebNov 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 … http://www-personal.umich.edu/~asnowden/notes/gz/L01.pdf

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 …

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 … sigma new lenses for sonyWeb2 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 ... the printery house catalog christmas cardsWebGross{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 … the printery holland michiganWebTélécharger 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 ... sigman flowersWebDec 31, 2024 · This formula over \(\mathscr {X}\) (which is an identity of functionals on some universal ordinary automorphic representations) specialises at classical points to all the Gross–Zagier formulas ... the printery house conception abbeyWebWe 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 … the printery house couponWeba higher analog of the formula of Gross and Zagier (see Corollary 0.3.2 of [Z]), and applying our argument below to this situation, one gets a variant of Theorem A determining (the motive of) f by the heights of the f-components of (homologically trivial) Heegner cycles, assuming one of them has a non-trivial height. sigma news today