Vol. 4, No. 8, 2010

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

Volume 13
Issue 5, 995–1242
Issue 4, 749–993
Issue 3, 531–747
Issue 2, 251–530
Issue 1, 1–249

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
Editorial Login
Ethics Statement
Author Index
To Appear
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Other MSP Journals
Remarks on modular symbols for Maass wave forms

Yuri I. Manin

Vol. 4 (2010), No. 8, 1091–1114

In this paper I introduce modular symbols for Maass wave cusp forms. They appear in the guise of finitely additive functions on the boolean algebra generated by intervals with nonpositive rational ends, with values in analytic functions (pseudomeasures in the sense of Manin and Marcolli). We explain the basic issues and draw an analogy with the p-adic case. We then construct the new modular symbols, followed by the related Lévy–Mellin transforms. This work builds on the fundamental study of Lewis and Zagier (2001).

To Professor F. Hirzebruch, with friendship and admiration, for his anniversary.

Maass modular forms, modular symbols
Mathematical Subject Classification 2000
Primary: 11F37
Received: 12 January 2010
Accepted: 1 October 2010
Published: 24 February 2011
Yuri I. Manin
Max-Planck-Institut für Mathematik
Vivatsgasse 7
D-53111 Bonn
Department of Mathematics
Northwestern University
Evanston, IL 60208-2730
United States