Notes on gross-zagier formula pdf
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 ... 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
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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 …
http://davidrenshawhansen.com/gztalk.pdf 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.
http://math.columbia.edu/~goldfeld/GaussProblem.pdf http://library.msri.org/books/Book49/files/11ulmer.pdf
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 …
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 … cincinnati reds standings standings 2022Web4 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 … cincinnati reds starting pitcher tonightWebCUBE 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 cincinnati reds standings by yearWeb0(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 … cincinnati reds starting lineup 2021WebMay 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 … cincinnati reds starting pitchersWebtion 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 ... dhs threat huntingWebJun 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 … cincinnati reds st louis cardinals brawl