## Algebra & Number Theory

### On the algebraic structure of iterated integrals of quasimodular forms

Nils Matthes

#### Abstract

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.

#### Article information

Source
Algebra Number Theory, Volume 11, Number 9 (2017), 2113-2130.

Dates
Revised: 15 June 2017
Accepted: 8 September 2017
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.ant/1513730348

Digital Object Identifier
doi:10.2140/ant.2017.11.2113

Mathematical Reviews number (MathSciNet)
MR3735463

Zentralblatt MATH identifier
06818946

#### Citation

Matthes, Nils. On the algebraic structure of iterated integrals of quasimodular forms. Algebra Number Theory 11 (2017), no. 9, 2113--2130. doi:10.2140/ant.2017.11.2113. https://projecteuclid.org/euclid.ant/1513730348

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