Sums of the additive divisor problem type and the inner product method

The inner product approach to the additive divisor problem with its cusp form analogs is surveyed, and a spectral summation formula for convolution sums involving Fourier coefficients of Maass forms is derived. An application to subconvexity estimates for Rankin-Selberg L-functions is announced. Bibliography: 18 titles. Dedicated to the memory of Yu. V. Linnik Published in Zapiski Nauchnykh Seminarov POMI, Vol. 322, 2005, pp. 239–250.