Moments of L-functions and Liouville-Green method

Olga Balkanova; Dmitry Frolenkov

Moments of L-functions and Liouville-Green method

Number Theory 2018-12-04 v3 Classical Analysis and ODEs

Authors: Olga Balkanova , Dmitry Frolenkov

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.

Keywords

L-functions moments primitive forms central point Kuznetsov convolution formula Liouville-Green method

Cite

@article{arxiv.1610.03465,
  title  = {Moments of L-functions and Liouville-Green method},
  author = {Olga Balkanova and Dmitry Frolenkov},
  journal= {arXiv preprint arXiv:1610.03465},
  year   = {2018}
}

Comments

final version; to appear in JEMS

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