Open Access
Translator Disclaimer
2010 Remarks on modular symbols for Maass wave forms
Yuri I. Manin
Algebra Number Theory 4(8): 1091-1114 (2010). DOI: 10.2140/ant.2010.4.1091

Abstract

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).

Citation

Download Citation

Yuri I. Manin. "Remarks on modular symbols for Maass wave forms." Algebra Number Theory 4 (8) 1091 - 1114, 2010. https://doi.org/10.2140/ant.2010.4.1091

Information

Received: 12 January 2010; Accepted: 1 October 2010; Published: 2010
First available in Project Euclid: 20 December 2017

zbMATH: 1229.11079
MathSciNet: MR2832636
Digital Object Identifier: 10.2140/ant.2010.4.1091

Subjects:
Primary: 11F37

Keywords: Maass modular forms , modular symbols

Rights: Copyright © 2010 Mathematical Sciences Publishers

JOURNAL ARTICLE
24 PAGES


SHARE
Vol.4 • No. 8 • 2010
MSP
Back to Top