On the shifted convolution problem in mean
arXiv:1202.3906 · doi:10.1016/j.jnt.2012.03.007
Abstract
We study a mean value of the shifted convolution problem over the Hecke eigenvalues of a fixed non-holomorphic cusp form. We attain a result also for a weighted case. Furthermore, we point out that the proof yields analogous upper bounds for the shifted convolution problem over the Fourier coefficients of a fixed holomorphic cusp form in mean.
21 pages. arXiv admin note: text overlap with arXiv:1110.3950 . <- The mentioned overlap appears in the introduction and in the section concerning the needed notation and auxiliary, known lemmas, not in the proofs :)