AI 中文总结
研究模L函数在临界带中心处一阶导数矩，通过由本原二次特征构成的广义除数函数加权，证明其渐近公式，此前该公式仅在高阶导数或二面体形式特殊化下被证明。
AI 中文摘要
本文证明了模L函数在临界带中心处一阶导数矩的渐近公式，该矩由本原二次特征构成的广义除数函数加权。此前Munshi研究过此类矩，其在椭圆纤维化研究中自然出现。据我们所知，此类渐近公式仅在高阶导数情形或二面体形式的特殊化下得到证明。
英文摘要
In this paper, we prove an asymptotic formula for the moment of the first order derivative of modular $L$-functions at the center of the critical strip, weighted by generalized divisor functions formed by primitive quadratic characters. Such moments were previously studied by Munshi, which naturally arise in the study of elliptic fibration. To the best of our knowledge, such asymptotic formulae have only been proven in the setting of higher-order derivatives, or under the specialization to dihedral forms.
Comments15 pages, added acknowledgement
