Abstract We show that a positive proportion of the derivatives of L-functions associated to holomorphic cusp forms of large weight do not vanish at the central point. Specifically, by optimizing the choice of quadratic form in the mollified moments of the L-function, we prove that this proportion is at least 39%.

中文翻译：

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L-函数的导数在中心点不消失

摘要 我们表明，与大权重的全纯尖端形式相关的 L 函数的导数的正比例不会在中心点消失。具体来说，通过优化 L 函数软化矩中二次形式的选择，我们证明这个比例至少为 39%。