Convolution formula for the sums of generalized Dirichlet $L$-functions

Olga Balkanova; Dmitry Frolenkov

doi:10.4171/rmi/1106

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

Convolution formula for the sums of generalized Dirichlet $L$ -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

A subscription is required to access this article.

Abstract

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

Cite this article

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

DOI 10.4171/RMI/1106