Notes on gross-zagier formula pdf

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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 ... 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 …

Elliptic curves, L-functions, and CM-points

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 WebGROSS-ZAGIER REVISITED BRIAN CONRAD Contents 1. Introduction 1 2. Some properties of abelian schemes and modular curves 3 3. The Serre-Tate theorem and the Grothendieck … css table code

Introduction algebraic integer - Columbia University

http://math.columbia.edu/~goldfeld/GaussProblem.pdf 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, … 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 … css table bottom border only

The Gross-Zagier-Zhang formula over function fields

Heegner points and L-series (preliminaries)

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 WebToday 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 early 2000\u0027s boy bandsWebfor 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-Rankin triple convolution of three Hida families of modular forms. The main goal of this article is to describe and prove this ... css table every other row

"Webtion formula. Theorem A. For any unramiﬁed cuspidal automorphic representation π, and for any even r≥0, h[Shtr T1] π,[Sht r T2] i= Cr(π). Theorem A is the function ﬁeld analogue of the Gross-Kohnen-Zagier formula [5, Theorem B], but for higher order derivatives. The original Gross-Kohnen-Zagier formula corresponds to the case r= 1 over ... " - Notes on gross-zagier formula pdf

Notes on gross-zagier formula pdf

Elliptic Curves and Analogies Between Number Fields and …

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

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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 …

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

WebGross-Zagier-Zhang formula over function elds B: incoherent quaternion algebra over A F, i.e. division at odd number of places. B 1is division. Fix A E,!B. M U=F: Drinfeld modular curves, indexed by U ˆB . Hecke action: B acts on lim U M . A=F: abelian variety such that (up to twist by a character) ˇ A:= lim! U Hom(J(M U);A) C = JL B (˙): t ... 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 …

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 …

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 … css table dynamic column widthWeb1.1. 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 … early 2000\u0027s emo songsWebThis 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 … css table even columnshttp://www.mi.uni-koeln.de/%7Ewoodbury/research/GZ-classnotes.pdf css table editorWebCUBE 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 css table filterWebJun 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 … early 2000\u0027s female psycho killer moviesWebfor 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 ... css table first column