JournalsjemsVol. 23, No. 4pp. 1333–1380

Moments of LL-functions and the Liouville–Green method

  • Olga Balkanova

    Steklov Mathematical Institute, Moscow, Russia
  • Dmitry Frolenkov

    HSE University and Steklov Mathematical Institute, Moscow, Russian Federation
Moments of $L$-functions and the Liouville–Green method cover

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Abstract

We show that for at least 20% of primitive forms of level 1 and weight 4k,kN4k \to \infty, k \in \mathbb N, the associated LL-function at the central point is no less than (log k)2k)^{–2}. The key ingredients of our proof are the Kuznetsov convolution formula and the Liouville–Green method.

Cite this article

Olga Balkanova, Dmitry Frolenkov, Moments of LL-functions and the Liouville–Green method. J. Eur. Math. Soc. 23 (2021), no. 4, pp. 1333–1380

DOI 10.4171/JEMS/1035