  Conditionally on the Riemann hypothesis we prove asymptotic formulae for mean
values of various long Dirichlet polynomials involving the von Mangoldt
function. Our results avoid the use of correlation sum estimates although in
addition to the Riemann hypothesis we must assume that our Dirichlet
polynomials have weights from a specific class whose transforms are
sufficiently concentrated near the origin. We also give large deviation
estimates for these long Dirichlet polynomials.
