Notes on gross-zagier formula pdf
http://math.columbia.edu/~goldfeld/GaussProblem.pdf 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
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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 ... http://library.msri.org/books/Book49/files/07zhang.pdf
Webfollowing Zagier’s computations, we will instead consider the curve 61.a1 and do all the computations from scratch. The notes are structured around the computation of this … 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 …
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 … 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 …
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
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 … bitblt srcandWebIn 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 ... bitblt vs windows graphics captureWebSep 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... darwich consulting ug gmbh i.gWebthe 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 ... bit bluetoothWebHere 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 … darwich meats \\u0026 coWebGross{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 … bitblt win10WebThe 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. bitblock free