## Abstract

For a prime p ≡ 3 (mod 4) and m ≥ 2, Romik raised a question about whether the Taylor coefficients around^{√}−1 of the classical Jacobi theta function θ_{3} eventually vanish modulo p^{m}. This question can be extended to a class of modular forms of half-integral weight on Γ_{1}(4) and CM points; in this paper, we prove an affirmative answer to it for primes p ≥ 5. Our result is also a generalization of the results of Larson and Smith for modular forms of integral weight on SL_{2}(Z).

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

Pages (from-to) | 23-38 |

Number of pages | 16 |

Journal | Taiwanese Journal of Mathematics |

Volume | 27 |

Issue number | 1 |

DOIs | |

State | Published - Feb 2023 |

### Bibliographical note

Publisher Copyright:© 2023, Mathematical Society of the Rep. of China. All rights reserved.

## Keywords

- Taylor coefficients
- congruences
- modular forms

## Fingerprint

Dive into the research topics of 'p-adic Properties for Taylor Coefficients of Half-integral Weight Modular Forms on Γ_{1}(4)'. Together they form a unique fingerprint.