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자연과학대학
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Journal papers
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p-adic Properties for Taylor Coefficients of Half-integral Weight Modular Forms on Γ1(4)
Title
p-adic Properties for Taylor Coefficients of Half-integral Weight Modular Forms on Γ1(4)
Authors
Kim J.
;
Lee Y.
Ewha Authors
이윤진
;
김지구
SCOPUS Author ID
이윤진
; 김지구
Issue Date
2023
Journal Title
Taiwanese Journal of Mathematics
ISSN
1027-5487
Citation
Taiwanese Journal of Mathematics vol. 27, no. 1, pp. 23 - 38
Keywords
congruences
;
modular forms
;
Taylor coefficients
Publisher
Mathematical Society of the Rep. of China
Indexed
SCIE; SCOPUS
Document Type
Article
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). © 2023, Mathematical Society of the Rep. of China. All rights reserved.
DOI
10.11650/tjm/220802
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