In this paper we calculate the asymptotics of various moments of the central values of Rankin-Selberg convolution L-functions of large level, thus generalizing the results and methods of W. Duke, J. Friedlander, and H. Iwaniec and of the authors. Consequences include convexity-breaking bounds, nonvanishing of a positive proportion of central values, and linear independence results for certain Hecke operators.
E. Kowalski. P. Michel. J. VanderKam. "Rankin-Selberg L-functions in the level aspect." Duke Math. J. 114 (1) 123 - 191, 15 July 2002. https://doi.org/10.1215/S0012-7094-02-11416-1