Vol. 11, No. 9, 2017

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

Volume 12
Issue 5, 1001–1309
Issue 4, 751–999
Issue 3, 493–750
Issue 2, 227–492
Issue 1, 1–225

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
Subscriptions
Editorial Board
Editors' Addresses
Editors' Interests
Scientific Advantages
Submission Guidelines
Submission Form
Editorial Login
Author Index
To Appear
 
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
On the algebraic structure of iterated integrals of quasimodular forms

Nils Matthes

Vol. 11 (2017), No. 9, 2113–2130
Abstract

We study the algebra QM of iterated integrals of quasimodular forms for SL2(), which is the smallest extension of the algebra QM of quasimodular forms which is closed under integration. We prove that QM is a polynomial algebra in infinitely many variables, given by Lyndon words on certain monomials in Eisenstein series. We also prove an analogous result for the M-subalgebra M of QM of iterated integrals of modular forms.

Keywords
quasimodular forms, iterated integrals
Mathematical Subject Classification 2010
Primary: 11F11
Secondary: 11F67
Milestones
Received: 8 November 2016
Revised: 15 June 2017
Accepted: 8 September 2017
Published: 2 December 2017
Authors
Nils Matthes
Max-Planck-Institut für Mathematik
Bonn
Germany