On double shifted convolution sum of $SL(2,\mathbb{Z})$ Hecke eigen forms

Abstract

Let ${\lambda }_i(n)$ $i=1,2,3$ denote the normalised Fourier coefficients of holomorphic eigenform or Maass cusp form. In this paper we shall consider the sum: \[ S:= \frac{1}{H}\sum_{h\leq H} V\left( \frac{h}{H}\right)\sum_{n\leq N} λ_1 (n) λ_2 (n+h) λ_3 (n+ 2h)W\left( \frac{n}{N} \right), \] \noindent where $V$ and $W$ are smooth bump functions, supported on $[1,2]$. We shall prove a nontrivial upper bound, under the assumption that $H\ge N^{1/2+\epsilon }$.

References in corpus (1)

• Triple correlations of Fourier coefficients of cusp forms

Cited by in corpus (1)

• Averages of shifted convolution sums for $GL(3)\times GL(2)$