Convolution formula for the sums of generalized Dirichlet -functions
Olga Balkanova
Chalmers University of Technology, Göteborg, SwedenDmitry Frolenkov
Khabarovsk Division of the Institute for Applied Mathematics and Steklov Mathematical Institute, Moscow, Russian Federat
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Abstract
Using the Kuznetsov trace formula, we prove a spectral decomposition for the sums of generalized Dirichlet -functions. Among applications are an explicit formula relating norms of prime geodesics to moments of symmetric square -functions and an asymptotic expansion for the average of central values of generalized Dirichlet -functions.
Cite this article
Olga Balkanova, Dmitry Frolenkov, Convolution formula for the sums of generalized Dirichlet -functions. Rev. Mat. Iberoam. 35 (2019), no. 7, pp. 1973–1995
DOI 10.4171/RMI/1106