Vol. 11, No. 9, 2017

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On the algebraic structure of iterated integrals of quasimodular forms

Nils Matthes

Vol. 11 (2017), No. 9, 2113–2130

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.

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