Notes on gross-zagier formula pdf

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August undefined, 2024

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

Gross-Zagier Formula on Shimura Curves, Hardcover by Yuan, …

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 … 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 … t shirts prints design

Introduction - University of Washington

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 ... WebDec 31, 2024 · David Loeffler, R. Rockwood, Sarah Livia Zerbes. Mathematics. 2024. We prove a “twist-compatibility” result for p-adic families of cohomology classes associated to symmetric spaces. This shows that a single family of classes (lying in a finitely-generated Iwasawa…. Expand. 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. phil robertson\u0027s new book

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

Gross{Zagier formula and arithmetic fundamental lemma

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 ... 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... t shirts print near meWebThis 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 … phil robertson\u0027s daughter\u0027s mother

"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 ... " - Notes on gross-zagier formula pdf

Notes on gross-zagier formula pdf

Heegner points and L-series (preliminaries)

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

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WebSep 1, 2024 · Request PDF Revisiting the Gross–Zagier discriminant formula We derive a formula for the discriminant of the ring class polynomial of conductor N associated to the … 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 …

http://davidrenshawhansen.com/gztalk.pdf 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 ...

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 … 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

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 …

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 … t shirts print shop near meWebGross-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 ... t shirts print shopsWebThis 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 … t shirts print on demandWebon 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 … t shirts printsWebThe 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, … phil robertson without a beardWebGross{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 … phil robertson videos youtubeWebThe 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 … phil robertson\u0027s daughter phyllis