Vol. 12, No. 3, 2018

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

Volume 12
Issue 6, 1311–1557
Issue 5, 1001–1309
Issue 4, 751–999
Issue 3, 493–750
Issue 2, 227–492
Issue 1, 1–225

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
Subscriptions
Editorial Board
Editors' Addresses
Editors' Interests
Scientific Advantages
Submission Guidelines
Submission Form
Editorial Login
Author Index
To Appear
 
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Algebraic de Rham theory for weakly holomorphic modular forms of level one

Francis Brown and Richard Hain

Vol. 12 (2018), No. 3, 723–750
Abstract

We establish an Eichler–Shimura isomorphism for weakly modular forms of level one. We do this by relating weakly modular forms with rational Fourier coefficients to the algebraic de Rham cohomology of the modular curve with twisted coefficients. This leads to formulae for the periods and quasiperiods of modular forms.

Keywords
weakly holomorphic modular form, algebraic de Rham cohomology
Mathematical Subject Classification 2010
Primary: 11F11
Secondary: 11F23, 11F25, 11F67
Milestones
Received: 3 August 2017
Revised: 22 December 2017
Accepted: 22 January 2018
Published: 12 June 2018
Authors
Francis Brown
All Souls College
Oxford
United Kingdom
Richard Hain
Department of Mathematics
Duke University
Durham, NC
United States