On double shifted convolution sum of SL(2,Z) Hecke eigenforms

Let λi(n), i=1,2,3, denote the normalized Fourier coefficients of a holomorphic eigenform or Maass cusp form. In this paper we shall consider the sum:S:=1H∑H≤h≤2HV(hH)×∑N≤n≤2Nλ1(n)λ2(n+h)λ3(n+2h)W(nN), where V and W are smooth bump functions, supported on [1,2]. We shall prove a nontrivial upper bound, under the assumption that H≥N1/2+ϵ.