Algebra & Number Theory

On the algebraic structure of iterated integrals of quasimodular forms

Nils Matthes

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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.

Article information

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

Received: 8 November 2016
Revised: 15 June 2017
Accepted: 8 September 2017
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11F11: Holomorphic modular forms of integral weight
Secondary: 11F67: Special values of automorphic $L$-series, periods of modular forms, cohomology, modular symbols

quasimodular forms iterated integrals


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.

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