The cubic moment of central L -values in the weight aspect

Motivated by the list of problems for moments of L -functions due to Hamieh et al. [7], we prove an asymptotic formula for the cubic moment of central L -values associated to holomorphic cusp forms of level one, where the weights k lie in a short interval K - Δ < k < K + Δ with K ε ≤ Δ ≤ K 1 - ε , as K → ∞ .