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.
Original language | English |
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Journal | Transactions of the American Mathematical Society |
Volume | 375 |
Issue number | 2 |
Pages (from-to) | 1443-1460 |
Number of pages | 18 |
ISSN | 0002-9947 |
DOIs | |
Publication status | Published - 2022 |
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© 2021 American Mathematical Society.
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