Central value of the symmetric square L-functions related to Hecke–Maass forms

The first moment of Maass form symmetric square L-functions

“…Theorem 1.2 improves the results of Ng [13,Theorem 7.1.1] and Tang [15]. The proof of Theorems 1.1 and 1.2 is based on the method of analytic continuation.…”

Prime geodesics and averages of the Zagier $L$-series

“…Maybe surprisingly, in order to make the argument work we need the existence of a symmetric square L-function with non-vanishing central value. This is ensured by an asymptotic formula for the first moment of symmetric square L-functions, see [26, Theorem 7.1.1], [30] and [1].…”