We prove the best possible upper bounds of the gaps between non-vanishing Fourier coefficients of half-integral weight cuspforms. This improves the works of Balog–Ono and Thorner. We also show an asymptotic formula of central modular $L$-values for short intervals.

中文翻译：

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半积分权重尖点的傅立叶系数不消失问题

我们证明了半积分权重尖点形状的非零傅立叶系数之间的间隙的最佳可能上限。这改进了巴洛格-奥诺和托纳的作品。我们还展示了中心模的渐近公式$L$- 短间隔的值。