This comprehensive account of the Gross-Zagier formula on Shimura curves over totally real fields relates the heights of Heegner points on abelian varieties to the derivatives of L-series. The formula will have new applications for the Birch and Swinnert
Kobayashi, S.: The \(p\) -adic Gross–Zagier formula for elliptic curves at supersingular primes. Invent. Math. 191 (3), 527–629 (2013) MathSciNet MATHDaniel Disegni, The p-adic Gross-Zagier formula on Shimura curves, Compos. Math. 153 (2017), no. 10, 1987-2074, DOI 10.1112/S0...
Gross substitutes, optimal transport and matching models_ Lecture 1 01:28:11 Gross substitutes, optimal transport and matching models_ Lecture 2 01:33:43 Gross substitutes, optimal transport and matching models_ Lecture 3 01:27:48 Non-realizability of polytopes via linear programming 54:47 ...
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This paper continues the investigation of the arithmetic of the curves CA: y2=xℓ+A and their Jacobians JA, where ℓ is an odd prime and A is an integer not divisible by ℓ, which was begun in an earlier paper. In the first part, we sketch how to extend the formula for the...
Abstract We describe the complex multiplication (CM) values of modular functions for\(\Gamma _0(N)\)whose divisor is given by a linear combination of Heegner divisors in terms of special cycles on the stack of CM elliptic curves. In particular, our results apply to Borcherds products of weig...
In this article, we study the Beilinson–Bloch–Kato conjecture for motives associated to Rankin–Selberg products of conjugate self-dual automorphic representations, within the framework of the Gan–Gross–Prasad conjecture. We show that if the central critical value of the Rankin–Selberg L-function...
Chapter One. Introduction and Statement of Main Results : The Gross-Zagier Formula on Shimura CurvesYuanXinyi / ZhangShouwu / ZhangWei
Moreover, if K is a real quadratic field, E is an elliptic curve over Q without complex multiplication and chi is a ring class character such that L-K (E, chi, 1) not equal 0, we prove a Gross-Zagier type formula relating Darmon points to a suitably defined algebraic part of L-K...
Moreover, if K is a real quadratic field, E is an elliptic curve over without complex multiplication and is a ring class character such that , we prove a Gross-Zagier type formula relating Darmon points to a suitably defined algebraic part of ; this generalizes results of Bertolini, Darmo...