Vol. 6, No. 3, 2012

Download this article
Download this article For screen
For printing
Recent Issues

Volume 18, 1 issue

Volume 17, 12 issues

Volume 16, 10 issues

Volume 15, 10 issues

Volume 14, 10 issues

Volume 13, 10 issues

Volume 12, 10 issues

Volume 11, 10 issues

Volume 10, 10 issues

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
About the Journal
Editorial Board
Editors’ Interests
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Author Index
To Appear
Other MSP Journals
$\mathscr{L}$-invariants and Shimura curves

Samit Dasgupta and Matthew Greenberg

Vol. 6 (2012), No. 3, 455–485

In earlier work, the second named author described how to extract Darmon-style -invariants from modular forms on Shimura curves that are special at p. In this paper, we show that these -invariants are preserved by the Jacquet–Langlands correspondence. As a consequence, we prove the second named author’s period conjecture in the case where the base field is . As a further application of our methods, we use integrals of Hida families to describe Stark–Heegner points in terms of a certain Abel–Jacobi map.

L-invariants, Shimura curves, Hida families, Stark–Heegner points
Mathematical Subject Classification 2000
Primary: 11F41
Secondary: 11G18, 11F67, 11F75
Received: 15 July 2010
Revised: 8 April 2011
Accepted: 23 May 2011
Published: 5 July 2012
Samit Dasgupta
Department of Mathematics
University of California, Santa Cruz
1156 High St
Santa Cruz, CA 95064
United States
Matthew Greenberg
Department of Mathematics and Statistics
University of Calgary
Calgary, AL T2N 1N4