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be the divisor function of order three. Let
be a Hecke–Maass form for
. Suppose that
th Hecke eigenvalue of
. Using the Voronoi summation formula for
and the Kuznetsov trace formula, we estimate a shifted convolution sum of
and show that
be an orthonormal basis of Hecke–Maass cusp forms with Laplace eigenvalue
th Fourier coefficient of
the divisor function of order three. In this paper, by the circle method and the Voronoi summation formula, the average value of the shifted convolution sum for
is considered, leading to the estimate