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On the algebraic structure of iterated integrals of quasimodular forms

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.
Publication status:
Published
Peer review status:
Peer reviewed
Version:
Publisher's version

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Publisher copy:
10.2140/ant.2017.11.2113

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Institution:
University of Oxford
Division:
MPLS Division
Department:
Mathematical Institute
Role:
Author
Publisher:
Mathematical Sciences Publishers Publisher's website
Journal:
Algebra and Number Theory Journal website
Volume:
11
Issue:
9
Pages:
2113-2130
Publication date:
2017-12-02
Acceptance date:
2017-09-08
DOI:
EISSN:
1944-7833
ISSN:
1937-0652
Pubs id:
pubs:952692
URN:
uri:aaef8f69-7e34-402a-ae89-1e2062208d25
UUID:
uuid:aaef8f69-7e34-402a-ae89-1e2062208d25
Local pid:
pubs:952692
Language:
English
Keywords:

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