Notes on gross-zagier formula pdf

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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 … 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 …

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WebGROSS-ZAGIER FORMULA NOTES TAKEN BY MIKE WOODBURY These are notes taken in Tonghai Yang’s course titled “The Gross-Zagier For-mula” at the University of Wisconsin … 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 cryptool2教程

Revisiting the Gross–Zagier discriminant formula Request PDF

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 ... WebDec 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 ... cryptool2数字签名

The universal p-adic Gross--Zagier formula - ResearchGate

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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 … 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 … dutch banking corporation crosswordWebSep 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... cryptool下载教程

"WebThis general formula applies to arbitrary cuspidal automorphic representations of GL2over totally real ﬁelds holomorphic of weight 2. In this paper, over global function ﬁelds of … " - Notes on gross-zagier formula pdf

Notes on gross-zagier formula pdf

Web1.1. 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 … http://library.msri.org/books/Book49/files/11ulmer.pdf

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http://math.columbia.edu/~goldfeld/GaussProblem.pdf 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 …

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

WebGross–Zagier Formula for GL(2), II SHOU-WU ZHANG Contents 1. Introduction and Notation 191 2. Automorphic Forms 195 3. Weights and Levels 197 4. Automorphic L-Series 199 5. …

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 ... dutch banket recipe easyhttp://davidrenshawhansen.com/gztalk.pdf cryptoonWebThe 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 … dutch banket pastryWebIn 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 ... cryptoon goonz openseaWebJun 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 … cryptoon goonzWebThis comprehensive account of the Gross-Zagier formula on Shimura curves over totally real fields relates the heights of Heegner points on abelian varieties to ... cryptool安装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 ... cryptoon goonz clothing