p-adic Properties for Taylor Coefficients of Half-integral Weight Modular Forms on Γ1(4)
- 주제(키워드) congruences , modular forms , Taylor coefficients
- 관리정보기술 faculty
- 등재 SCIE, SCOPUS
- 발행기관 Mathematical Society of the Rep. of China
- 발행년도 2023
- 총서유형 Journal
- URI http://www.dcollection.net/handler/ewha/000000205874
- 본문언어 영어
- Published As https://doi.org/10.11650/tjm/220802
초록/요약
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). © 2023, Mathematical Society of the Rep. of China. All rights reserved.
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