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Moments of $L$-functions and the Liouville–Green method
Journal of the European Mathematical Society ( IF 2.6 ) Pub Date : 2021-01-05 , DOI: 10.4171/jems/1035
Olga Balkanova 1 , Dmitry Frolenkov 2
Affiliation  

We show that the percentage of primitive forms of level one and weight $4k\rightarrow \infty$ for which the associated $L$-function at the central point is no less than $(\log{k})^{-2}$ is at least 20%. The key ingredients of our proof are the Kuznetsov convolution formula and the Liouville-Green method.

中文翻译:

$L$ 函数的矩和 Liouville-Green 方法

我们证明一级和权重 $4k\rightarrow\infty$ 的原始形式的百分比在中心点相关联的 $L$ 函数不小于 $(\log{k})^{-2} $ 至少为 20%。我们证明的关键要素是 Kuznetsov 卷积公式和 Liouville-Green 方法。
更新日期:2021-01-05
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