generating series. Using Arakelov theory and the modularity of Kudla's generating series, the proof of the Gross-Zagier formula is reduced to local formulas.\nThe Gross-Zagier Formula on Shimura Curves will be of great use to students wishing to enter this area and to those already working in it.
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 Swinnerton-Dyer conjecture and Diophantine equations. ...
Yuan, X., Zhang, S.-W., Zhang, W.: The Gross–Zagier Formula on Shimura Curves. Annals of Mathematics Studies, vol. 184. Princeton University Press, Princeton (2013) MATH Google Scholar Zhang, S.: The nonvanishing of L(1) for the L-series of some elliptic curves. Adv. Math. (...
In fact, in Disegni's work on the p-adic Gross–Zagier formula for Shimura curves in the inert case [5], a crucial ingredient are Hecke correspondences for arbitrarily deep level. One spin-off of the consideration of the AFL conjecture for the spherical Hecke algebra is that it naturally ...
Extensions of the Gross-Zagier formula - Kartik Prasanna 01:02:01 Group theoretic applications of the large sieve method - Chen Meiri 38:24 Heegaard Biagrams and Holomorphic Disks - Peter Ozsváth 32:20 Inferring Parking Occupancy and Search from Parking Payment Data - Daniel Jordon 42:09...
Gross-Zagier formula for Shimura curves (Shou-Wu Zhang) 2-3 58:02 Gross-Zagier formula for Shimura curves (Shou-Wu Zhang) 3-3 54:35 Sur les déformations p-adiques des formes de Saito-Kurokawa (Eric Urban) 1-3 01:09:42 Sur les déformations p-adiques des formes de Saito-Kurokawa...
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...
This chapter is in the book The Gross-Zagier Formula on Shimura Curves Chapter SixDerivative of the Analytic KernelLetφ=φf⊗φ∞∈S(V×A×) be a Schwartz function. Assume that thearchimedean partφ∞is standard, and that the finite partφfis invariant underthe action ofK=U×Ufor some...
Daniel Disegni, The p-adic Gross-Zagier formula on Shimura curves, Compos. Math. 153 (2017), no. 10, 1987-2074, DOI 10.1112/S0010437X17007308. MR3692745 ↑3, 12D. Disegni, The p-adic Gross-Zagier formula on Shimura curves, Compos. Math. 153-10 (2017), 1987-2074....
THE p -ADIC GROSS–ZAGIER FORMULA ON SHIMURA CURVES, II: NONSPLIT PRIMES – CORRIGENDUMdoi:10.1017/S147474802400001XDisegni, DanielJournal of the Institute of Mathematics of Jussieu