p-adic properties for Taylor coecients of half-integral weight modular forms on Γ_1(4)

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p-adic properties for Taylor coecients of half-integral weight modular forms on Γ_1(4)

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구분 Rookies Pitch (BK21 FOUR 신진연구자 연구발표회)
일정 2021-10-19(화) 16:30~17:10
세미나실 129동 101호
강연자 김지구 (이화여대)
담당교수 서인석
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※ 시간: 16:40-17:10 ※ Zomm 병행: https://snu-ac-kr.zoom.us/j/2473239867 For an integer m ≥ 2 and a prime p ≡ 3 (mod 4), Romik raised a question about whether the Taylor coefficients around √ −1 of the classical Jacobi theta function θ3 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 talk, we show an affirmative answer to it for primes p ≥ 5. This is a joint work with Yoonjin Lee.

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