On the algebraic structure of iterated integrals of quasimodular forms - Matthes, N (Mathematical Sciences Publishers, 2017)
We study the algebra IQM of iterated integrals of quasimodular forms for SL2.Z/, which is the smallest extension of the algebra QM* of quasimodular forms which is closed under integration. We prove that IQM 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 IM of IQM of iterated integrals of modular forms.