### Abstract

Recently, Bruinier, Kohnen and Ono obtained an explicit description of the action of the theta-operator on meromorphic modular forms f on SL _{2}(ℤ) in terms of the values of modular functions at points in the divisor of f. Using this result, they studied the exponents in the infinite product expansion of a modular form and recurrence relations for Fourier coefficients of a modular form. In this paper, we extend these results to meromorphic modular forms on Γ_{0}(N) for an arbitrary positive integer N >1.

Original language | English |
---|---|

Pages (from-to) | 3393-3403 |

Number of pages | 11 |

Journal | Proceedings of the American Mathematical Society |

Volume | 138 |

Issue number | 10 |

DOIs | |

Publication status | Published - 2010 Oct 1 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

**Poincaré series and the divisors of modular forms.** / Choi, Dohoon.

Research output: Contribution to journal › Article

*Proceedings of the American Mathematical Society*, vol. 138, no. 10, pp. 3393-3403. https://doi.org/10.1090/S0002-9939-2010-10133-8

}

TY - JOUR

T1 - Poincaré series and the divisors of modular forms

AU - Choi, Dohoon

PY - 2010/10/1

Y1 - 2010/10/1

N2 - Recently, Bruinier, Kohnen and Ono obtained an explicit description of the action of the theta-operator on meromorphic modular forms f on SL 2(ℤ) in terms of the values of modular functions at points in the divisor of f. Using this result, they studied the exponents in the infinite product expansion of a modular form and recurrence relations for Fourier coefficients of a modular form. In this paper, we extend these results to meromorphic modular forms on Γ0(N) for an arbitrary positive integer N >1.

AB - Recently, Bruinier, Kohnen and Ono obtained an explicit description of the action of the theta-operator on meromorphic modular forms f on SL 2(ℤ) in terms of the values of modular functions at points in the divisor of f. Using this result, they studied the exponents in the infinite product expansion of a modular form and recurrence relations for Fourier coefficients of a modular form. In this paper, we extend these results to meromorphic modular forms on Γ0(N) for an arbitrary positive integer N >1.

UR - http://www.scopus.com/inward/record.url?scp=77955652416&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77955652416&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-2010-10133-8

DO - 10.1090/S0002-9939-2010-10133-8

M3 - Article

VL - 138

SP - 3393

EP - 3403

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 10

ER -