Moments of \(L\)-functions and the Liouville-Green method (Q2031670)

Summary: We show that for at least 20\% of primitive forms of level 1 and weight \(4k\to\infty\), \(k\in\mathbb{N}\), the associated \(L\)-function at the central point is no less than \((\log k)^{-2}\). The key ingredients of our proof are the Kuznetsov convolution formula and the Liouville-Green method.