@article{4eac40f23a4f4a889878358211d82c8a,
title = "p-adic Properties for Taylor Coefficients of Half-integral Weight Modular Forms on Γ1(4)",
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 θ3 eventually vanish modulo pm. This question can be extended to a class of modular forms of half-integral weight on Γ1(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 SL2(Z).",
keywords = "Taylor coefficients, congruences, modular forms",
author = "Jigu Kim and Yoonjin Lee",
note = "Funding Information: The authors thank the reviewers for the valuable suggestions. The authors were supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (Grant No. 2019R1A6A1A11051177). J. Kim was also supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (Grant No. 2020R1I1A1A01074746), and Y. Lee was also supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) (NRF-2022R1A2C1003203). Publisher Copyright: {\textcopyright} 2023, Mathematical Society of the Rep. of China. All rights reserved.",
year = "2023",
month = feb,
doi = "10.11650/tjm/220802",
language = "English",
volume = "27",
pages = "23--38",
journal = "Taiwanese Journal of Mathematics",
issn = "1027-5487",
publisher = "Mathematical Society of the Rep. of China",
number = "1",
}