On some mean square estimates in the Rankin-Selberg problem

An overview of the classical Rankin-Selberg problem involving the asymptotic formula for sums of coefficients of holomorphic cusp forms is given. We also study the function $\Delta(x;\xi) (0\le\xi\le1)$, the error term in the Rankin-Selberg problem weighted by $\xi$-th power of the logarithm. Mean square estimates for $\Delta(x;\xi)$ are proved.Comment: 12 page

Estimates of convolutions of certain number-theoretic error terms

Several estimates for the convolution function C [f(x)]:=∫1xf(y) f(x/y)(dy/y) and its iterates are obtained when f(x) is a suitable number-theoretic error term. We deal with the case of the asymptotic formula for ∫0T|ζ(1/2+it)|2kdt(k=1,2), the general Dirichlet divisor problem, the problem of nonisomorphic Abelian groups of given order, and the Rankin-Selberg convolution