Notes on gross-zagier formula pdf

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

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

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 ... 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 por vida therapeutics https://readysetbathrooms.com

DIAGONAL CYCLES AND EULER SYSTEMS I: A p-ADIC GROSS …

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 … 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 ... 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 ... irina tedrick

The Gross-Zagier formula: a brief introduction

Category:Revisiting the Gross–Zagier discriminant formula Request PDF

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Notes on gross-zagier formula pdf

The Gross–Kohnen–Zagier Theorem over Totally Real Fields

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

Notes on gross-zagier formula pdf

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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 ... 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 …

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. … Weba 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.

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

http://www.mi.uni-koeln.de/%7Ewoodbury/research/GZ-classnotes.pdf

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 por una cabeza orchestra sheet musicWebSep 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 … por utilityWebGROSS-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 … por un amor in englishWebThis 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 … irina tailor shopWebWe 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 … irina tcherniakWebHere 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 … por vs para cheat sheetWebThe 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. irina starshenbaum russian name