p-Adic limit of the Fourier coefficients of weakly holomorphic modular forms of half integral weight

D. Choi; Y. Choie

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p-Adic limit of the Fourier coefficients of weakly holomorphic modular forms of half integral weight

机译：半整数权的弱全纯模形式的Fourier系数的p-Adic极限

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Serre obtained the p-adic limit of the integral Fourier coefficients of modular forms on SL ₂(ℤ) for p = 2, 3, 5, 7. In this paper, we extend the result of Serre to weakly holomorphic modular forms of half integral weight on Γ₀(4N) for N = 1, 2, 4. The proof is based on linear relations among Fourier coefficients of modular forms of half integral weight. As applications to our main result, we obtain congruences on various modular objects, such as those for Borcherds exponents, for Fourier coefficients of quotients of Eisentein series and for Fourier coefficients of Siegel modular forms on the Maass Space.

机译：Serre获得了p = 2，3，5，7时SL _{2 （ℤ）上模形式积分傅里叶系数的p-adic极限。在本文中，我们将Serre的结果扩展为对于N = 1、2、4，在Γ_{0 （4N）上具有半整数权重的弱全纯模形式。证明是基于半整数权重的模块化形式的Fourier系数之间的线性关系。作为对我们主要结果的应用，我们在各种模块对象上取得了等价性，例如在Boassds指数上的那些，在Eassentein级数上的商的傅里叶系数以及在Maass空间上的Siegel模形式的傅里叶系数。}}

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《Israel Journal of Mathematics》 |2010年第1期|p.61-83|共23页
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D. Choi; Y. Choie;
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1. p-Adic limit of the Fourier coefficients of weakly holomorphic modular forms of half integral weight [J] . Choi D, Choie Y Israel Journal of Mathematics . 2010,第Null期

机译：半整数权的弱全纯模形式的Fourier系数的p-Adic极限
2. p-adic properties of coefficients of basis for the space of weakly holomorphic modular forms of weight 2 [J] . Soyoung CHOI Proceedings of the Japan Academy, Series A. Mathematical Sciences . 2012,第1期

机译：权重2的弱全纯模形式空间的基础系数的p-adic性质
3. Fourier coefficients of modular forms of half integral weight, periods of modular forms and the special values of zeta functions [J] . Hisashi Kojima Hiroshima Mathematical Journal . 1997,第2期

机译：半积分权重的模块化形式的傅立叶系数，模块化形式的周期和zeta函数的特殊值
4. RADIAL LIMIT OF LACUNARY FOURIER SERIES WITH COEFFICIENTS IN NON-COMMUTATIVE SYMMETRIC SPACES [C] . CAMIL MUSCALU Report on the Sixteenth conference on operator theory . 1996

机译：非对换对称空间中具有系数的Laoary Fourier级数的径向极限
5. The Fourier coefficients of modular forms and modular integrals having small positive weight. [D] . Pribitkin, Wladimar de Azevedo. 1995

机译：模块化形式和模块化积分的傅里叶系数具有较小的正权重。
6. p-adic coupling of mock modular forms and shadows [O] . Pavel Guerzhoy, Zachary A. Kent, Ken Ono 2010

机译：模拟模块形式和阴影的p-adic耦合
7. p-ADIC LIMIT OF THE FOURIER COEFFICIENTS OF WEAKLY HOLOMORPHIC MODULAR FORMS OF HALF INTEGRAL WEIGHT [O] . D. Choi, Y. Choie 2013

机译：半正整重的弱全同模量形式的傅立叶系数的p-aDIC极限
8. A TABLE OF WIGNER 9j COEFFICIENTS FOR INTEGRAL AND HALF-INTEGRAL VALUES OF THE PARAMETERS [R] . Kenneth Smith, John W. Stevenson 1957

机译：WEGER 9j系数表，用于参数的积分和半积分值

p-Adic limit of the Fourier coefficients of weakly holomorphic modular forms of half integral weight

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