Algebra & Number Theory
- Algebra Number Theory
- Volume 4, Number 8 (2010), 1091-1114.
Remarks on modular symbols for Maass wave forms
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 -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).
Algebra Number Theory, Volume 4, Number 8 (2010), 1091-1114.
Received: 12 January 2010
Accepted: 1 October 2010
First available in Project Euclid: 20 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 11F37: Forms of half-integer weight; nonholomorphic modular forms
Manin, Yuri I. Remarks on modular symbols for Maass wave forms. Algebra Number Theory 4 (2010), no. 8, 1091--1114. doi:10.2140/ant.2010.4.1091. https://projecteuclid.org/euclid.ant/1513729611