Vol. 315, No. 1, 2021

Download this article
Download this article For screen
For printing
Recent Issues
Vol. 315: 1  2
Vol. 314: 1  2
Vol. 313: 1  2
Vol. 312: 1  2
Vol. 311: 1  2
Vol. 310: 1  2
Vol. 309: 1  2
Vol. 308: 1  2
Online Archive
The Journal
Editorial Board
Submission Guidelines
Submission Form
Policies for Authors
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author Index
To Appear
Other MSP Journals
This article is available for purchase or by subscription. See below.
The index of a modular differential operator

William Duke

Vol. 315 (2021), No. 1, 45–73

The space of all weakly holomorphic modular forms and the space of all holomorphic period functions of a fixed weight for the modular group are realized as locally convex topological vector spaces that are topologically dual to each other. This framework is used to study the kernel and range of a linear differential operator that preserves modularity and to define and describe its adjoint. The main results are an index formula for such a differential operator that is holomorphic at infinity and the identification of the cokernel of the operator as a cohomology group of the modular group acting on the kernel.

PDF Access Denied

We have not been able to recognize your IP address as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recom­mendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

differential operator
Mathematical Subject Classification
Primary: 11F11
Secondary: 34M03
Received: 6 October 2020
Revised: 12 February 2021
Accepted: 25 September 2021
Published: 13 December 2021
William Duke
Mathematics Department
Los Angeles, CA
United States