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arXiv · 1610.03465

Moments of L-functions and Liouville-Green method

Olga Balkanova·Dmitry Frolenkov
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Abstract

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.

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Olga Balkanova, Dmitry Frolenkov. 2016-10-11. Moments of L-functions and Liouville-Green method. https://arxiv.org/abs/1610.03465

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