English

Remarks on modular symbols for Maass wave forms

Number Theory 2008-05-27 v2 Algebraic Geometry

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 L\'evy--Mellin transforms in the sec. 2. The whole paper is an extended footnote to the Lewis--Zagier fundamental study [LZ2].

Keywords

Cite

@article{arxiv.0803.3270,
  title  = {Remarks on modular symbols for Maass wave forms},
  author = {Yu I. Manin},
  journal= {arXiv preprint arXiv:0803.3270},
  year   = {2008}
}

Comments

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

R2 v1 2026-06-21T10:23:41.779Z