On the shifted convolution problem in mean

: Suvitie E

: 2012

Journal of Number Theory

: JOURNAL OF NUMBER THEORY

: J NUMBER THEORY

: 9

: 132

: 9

: 2046

: 2064

: 19

: 0022-314X

DOI: https://doi.org/10.1016/j.jnt.2012.03.007

over the Hecke eigenvalues of a fixed non-holomorphic cusp form with quantities N >= 1, 1 <= L <= N1-epsilon and 1 <= F << N-2/5. 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. (C) 2012 Elsevier Inc. All rights reserved.