Iterated primitives of meromorphic quasimodular forms for SL2(Z)
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We introduce and study iterated primitives of meromorphic quasimodular forms for SL2(Z), generalizing work of Manin and Brown for holomorphic modular forms. We prove that the algebra of iterated primitives of meromorphic quasimodular forms is naturally isomorphic to a certain explicit shuffle algebra. We deduce from this an Ax–Lindemann–Weierstrass type algebraic independence criterion for primitives of meromorphic quasimodular forms which includes a recent result of Paşol–Zudilin as a special case. We also study spaces of meromorphic modular forms with restricted poles, generalizing results of Guerzhoy in the weakly holomorphic case.
Originalsprog | Engelsk |
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Tidsskrift | Transactions of the American Mathematical Society |
Vol/bind | 375 |
Udgave nummer | 2 |
Sider (fra-til) | 1443-1460 |
Antal sider | 18 |
ISSN | 0002-9947 |
DOI | |
Status | Udgivet - 2022 |
Bibliografisk note
Funding Information:
Received by the editors January 27, 2021, and, in revised form, February 15, 2021, and July 10, 2021. 2020 Mathematics Subject Classification. Primary 11F37; Secondary 11F67. This project had received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 724638).
Publisher Copyright:
© 2021 American Mathematical Society.
ID: 345317175