Resumen de Convolution formula for the sums of generalized Dirichlet L-functions

Olga Balkanova, Dmitry Frolenkov

• 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.