JournalsrmiVol. 35, No. 7pp. 1973–1995

Convolution formula for the sums of generalized Dirichlet LL-functions

  • Olga Balkanova

    Chalmers University of Technology, Göteborg, Sweden
  • Dmitry Frolenkov

    Khabarovsk Division of the Institute for Applied Mathematics and Steklov Mathematical Institute, Moscow, Russian Federat
Convolution formula for the sums of generalized Dirichlet $L$-functions cover

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Abstract

Using the Kuznetsov trace formula, we prove a spectral decomposition for the sums of generalized Dirichlet LL-functions. Among applications are an explicit formula relating norms of prime geodesics to moments of symmetric square LL-functions and an asymptotic expansion for the average of central values of generalized Dirichlet LL-functions.

Cite this article

Olga Balkanova, Dmitry Frolenkov, Convolution formula for the sums of generalized Dirichlet LL-functions. Rev. Mat. Iberoam. 35 (2019), no. 7, pp. 1973–1995

DOI 10.4171/RMI/1106