Remarks on modular symbols for Maass wave forms

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 non--positive rational ends, with values in analytic functions (pseudo--measures in the sense of [MaMar2]). After explaining the basic issues and analogies in the extended Introduction, I construct modular symbols in the sec. 1 and the related Lévy--Mellin transforms in the sec. 2. The whole paper is an extended footnote to the Lewis--Zagier fundamental study [LZ2].

25 pages. Typos fixed, a dedication to F. Hirzebruch added

References in corpus (1)

• Transfer operators for ${\Gamma }_0(n)$ and the Hecke operators for the period functions for $PSL(2,Z)$