A general divisor problem involving Hecke eigenvalues.

Let f(z) be a holomorphic or Maass cusp form for the full modular group S L (2 , Z) . In this paper, we consider the asymptotic behavior of the sums U w (x) = ∑ n ≤ x λ w , f × f (n) , which can be regarded as the general divisor problems considered by Kanemitsu et al. (Monatsh Math 136(1):17–34, 2002), and get some new results which improve previous results. [ABSTRACT FROM AUTHOR]