Moments of L-functions and Liouville-Green method
classification
🧮 math.NT
math.CA
keywords
liouville-greenmethodassociatedcentralconvolutionformsformulafunction
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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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