Iterated primitives of meromorphic quasimodular forms for  SL2(Z)

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Standard

Iterated primitives of meromorphic quasimodular forms for  SL2(Z). / Matthes, Nils.

I: Transactions of the American Mathematical Society, Bind 375, Nr. 2, 2022, s. 1443-1460.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Matthes, N 2022, 'Iterated primitives of meromorphic quasimodular forms for  SL2(Z)', Transactions of the American Mathematical Society, bind 375, nr. 2, s. 1443-1460. https://doi.org/10.1090/tran/8538

APA

Matthes, N. (2022). Iterated primitives of meromorphic quasimodular forms for  SL2(Z). Transactions of the American Mathematical Society, 375(2), 1443-1460. https://doi.org/10.1090/tran/8538

Vancouver

Matthes N. Iterated primitives of meromorphic quasimodular forms for  SL2(Z). Transactions of the American Mathematical Society. 2022;375(2):1443-1460. https://doi.org/10.1090/tran/8538

Author

Matthes, Nils. / Iterated primitives of meromorphic quasimodular forms for  SL2(Z). I: Transactions of the American Mathematical Society. 2022 ; Bind 375, Nr. 2. s. 1443-1460.

Bibtex

@article{c7b50a785e274911b17c3cbd93d95cb9,
title = "Iterated primitives of meromorphic quasimodular forms for  SL2(Z)",
abstract = "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 Pa{\c s}ol–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.",
author = "Nils Matthes",
note = "Publisher Copyright: {\textcopyright} 2021 American Mathematical Society.",
year = "2022",
doi = "10.1090/tran/8538",
language = "English",
volume = "375",
pages = "1443--1460",
journal = "Transactions of the American Mathematical Society",
issn = "0002-9947",
publisher = "American Mathematical Society",
number = "2",

}

RIS

TY - JOUR

T1 - Iterated primitives of meromorphic quasimodular forms for  SL2(Z)

AU - Matthes, Nils

N1 - Publisher Copyright: © 2021 American Mathematical Society.

PY - 2022

Y1 - 2022

N2 - 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.

AB - 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.

U2 - 10.1090/tran/8538

DO - 10.1090/tran/8538

M3 - Journal article

AN - SCOPUS:85124591463

VL - 375

SP - 1443

EP - 1460

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

SN - 0002-9947

IS - 2

ER -

ID: 345317175