## Abstract

Let q:=e^{2πiz}, where z∈H. For an even integer k, let f(z):=q^{h}∏_{m=1} ^{∞}(1−q^{m})^{c(m)} be a meromorphic modular form of weight k on Γ_{0}(N). For a positive integer m, let T_{m} be the mth Hecke operator and D be a divisor of a modular curve with level N. Both subjects, the exponents c(m)of a modular form and the distribution of the points in the support of T_{m}.D, have been widely investigated. When the level N is one, Bruinier, Kohnen, and Ono obtained, in terms of the values of j-invariant function, identities between the exponents c(m)of a modular form and the points in the support of T_{m}.D. In this paper, we extend this result to general Γ_{0}(N)in terms of values of harmonic weak Maass forms of weight 0. By the distribution of Hecke points, this applies to obtain an asymptotic behavior of convolutions of sums of divisors of an integer and sums of exponents of a modular form.

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

Pages (from-to) | 1046-1062 |

Number of pages | 17 |

Journal | Journal of Mathematical Analysis and Applications |

Volume | 477 |

Issue number | 2 |

Early online date | 6 May 2019 |

DOIs | |

Publication status | Published - 15 Sep 2019 |

## Keywords

- Distribution
- Harmonic weak Maass forms
- Hecke orbits