Abstract In this paper, we consider p -adic limits of β ? n g | U p 2 n $eta ^{-n}g|U_{p^{2}}^{n}$ for half-integral weight weakly holomorphic Hecke eigenforms g with eigenvalue λ ~( p )= β + β _(′) under T p 2 $Tphantom {dot {i}!}_{p^{2}}$ and prove that these equal classical Hecke eigenforms of the same weight. This result parallels the integral weight case, but requires a much more careful investigation due to a more complicated structure of half-integral weight weakly holomorphic Hecke eigenforms.
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机译：摘要在本文中，我们考虑β？的p -adic极限。克| U p 2 n $ beta ^ {-n} g | U_ {p ^ {2}} ^ {n} $对于特征值为λ〜（p）=β+β_（）的半整数权重弱全同形Hecke特征形g ′）在T p 2 $ T phantom { dot {i} ！} _ {p ^ {2}} $下，证明这些相等的经典Hecke特征形相等。该结果与积分权重的情况相似，但由于半积分权重的弱全同性Hecke本征形的结构更加复杂，因此需要进行更仔细的研究。
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