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Let Formula: see text be the Formula: see textth Fourier coefficient of Formula: see text Hecke–Maass cusp form, denoted as Formula: see text or the triple divisor function, denoted as Formula: see text. Let Formula: see text be an integer. In this paper, we establish an asymptotic formula for the sum Formula: see text where Formula: see text is either von Mangoldt function or identity function, and Formula: see text is a binary quadratic polynomial. When Formula: see text, then Formula: see text can be any bounded arithmetical function.
Chanana et al. (Mon,) studied this question.