  In this series we examine the calculation of the $2k$th moment and shifted
moments of the Riemann zeta-function on the critical line using long Dirichlet
polynomials and divisor correlations. The present paper begins the general
study of what we call Type II sums which utilize a circle method framework and
a convolution of shifted convolution sums to obtain all of the lower order
terms in the asymptotic formula for the mean square along $[T,2T]$ of a
Dirichlet polynomial of length up to $T^3$ with divisor functions as
coefficients.
