Estimates for sums of coefficients of Dirichlet series with functional equation (Q1417932)

It is well known how to draw conclusions on the sum function of the coefficients of a Dirichlet series if it is known that this series satisfies a functional equation of the Riemann type. The author proves estimates for the sum function (also over an arithmetic progression) under stronger conditions such as the validity of a formula of the Rankin-Selberg type for the mean square of the coefficients, or supposing that the twists of the series with certain Dirichlet characters satisfy a functional equation.