\(p\)-adic Rankin \(L\)-series and rational points on CM elliptic curves

DOI10.2140/pjm.2012.260.261zbMath1326.11026OpenAlexW2161621043MaRDI QIDQ1935334

Massimo Bertolini, Kartik Prasanna, Henri Darmon

Publication date: 15 February 2013

Published in: Pacific Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: http://msp.org/pjm/2012/260-2/p02.xhtml

zbMATH Keywords

elliptic curvesrational pointsHeegner points\(p\)-adic \(L\)-functionselliptic units\(p\)-adic Rankin \(L\)-series

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) (L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture (11G40)

Related Items (17)

Interpolation of generalized Heegner cycles in Coleman families ⋮ STARK POINTS AND -ADIC ITERATED INTEGRALS ATTACHED TO MODULAR FORMS OF WEIGHT ONE ⋮ \(p\)-adic \(L\)-functions and the coniveau filtration on Chow groups. With an appendix by Brian Conrad. ⋮ Approximations of the balanced triple product \(p\)-adic \(L\)-function ⋮ Report on the Birch and Swinnerton-Dyer conjecture ⋮ Generalized Heegner cycles and \(p\)-adic Rankin \(L\)-series. With an appendix by Brian Conrad ⋮ A $p$-adic Stark conjecture in the rank one setting ⋮ Geometry of the eigencurve at CM points and trivial zeros of Katz \(p\)-adic \(L\)-functions ⋮ Stark points and the Hida-Rankin \(p\)-adic \(L\)-function ⋮ Heegner point Kolyvagin system and Iwasawa main conjecture ⋮ On the non-vanishing of \(p\)-adic heights on CM abelian varieties, and the arithmetic of Katz \(p\)-adic \(L\)-functions ⋮ The exceptional zero phenomenon for elliptic units ⋮ On the non-triviality of the $p$-adic Abel–Jacobi image of generalised Heegner cycles modulo $p$, I: Modular curves ⋮ \(p\)-converse to a theorem of Gross-Zagier, Kolyvagin and Rubin ⋮ On anticyclotomic variants of the \(p\)-adic Birch and Swinnerton-Dyer conjecture ⋮ Heegner points and Beilinson-Kato elements: a conjecture of Perrin-Riou ⋮ \(p^{\infty}\)-Selmer groups and rational points on CM elliptic curves

This page was built for publication: \(p\)-adic Rankin \(L\)-series and rational points on CM elliptic curves