### Abstract

Bruinier and Ono classified cusp forms of half-integral weight F(z) := Σ^{∞}_{n=1} a(n)q^{n} ∈ S _{λ+1/2} (Γ_{0}(N),χ) ∩ ℤ[[q]] whose Fourier coefficients are not well distributed for modulo odd primes ℓ. Ahlgren and Boylan established bounds for the weight of such a cusp form and used these bounds to prove Newman's conjecture for the partition function for prime-power moduli. In this note, we give a simple proof of Ahlgren and Boylan's result on bounds of cusp forms of half-integral weight.

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

Pages (from-to) | 2683-2688 |

Number of pages | 6 |

Journal | Proceedings of the American Mathematical Society |

Volume | 136 |

Issue number | 8 |

DOIs | |

Publication status | Published - 2008 Aug 1 |

Externally published | Yes |

### Fingerprint

### Keywords

- Congruences
- Modular forms

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

**Modular forms of half-integral weight with few non-vanishing coefficients modulo ℓ.** / Choi, Dohoon.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Modular forms of half-integral weight with few non-vanishing coefficients modulo ℓ

AU - Choi, Dohoon

PY - 2008/8/1

Y1 - 2008/8/1

N2 - Bruinier and Ono classified cusp forms of half-integral weight F(z) := Σ∞n=1 a(n)qn ∈ S λ+1/2 (Γ0(N),χ) ∩ ℤ[[q]] whose Fourier coefficients are not well distributed for modulo odd primes ℓ. Ahlgren and Boylan established bounds for the weight of such a cusp form and used these bounds to prove Newman's conjecture for the partition function for prime-power moduli. In this note, we give a simple proof of Ahlgren and Boylan's result on bounds of cusp forms of half-integral weight.

AB - Bruinier and Ono classified cusp forms of half-integral weight F(z) := Σ∞n=1 a(n)qn ∈ S λ+1/2 (Γ0(N),χ) ∩ ℤ[[q]] whose Fourier coefficients are not well distributed for modulo odd primes ℓ. Ahlgren and Boylan established bounds for the weight of such a cusp form and used these bounds to prove Newman's conjecture for the partition function for prime-power moduli. In this note, we give a simple proof of Ahlgren and Boylan's result on bounds of cusp forms of half-integral weight.

KW - Congruences

KW - Modular forms

UR - http://www.scopus.com/inward/record.url?scp=77950851209&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77950851209&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-08-09195-8

DO - 10.1090/S0002-9939-08-09195-8

M3 - Article

AN - SCOPUS:77950851209

VL - 136

SP - 2683

EP - 2688

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 8

ER -