Sums of Values of Nonprincipal Characters over a Sequence of Shifted Primes

For a nonprincipal character χ modulo D, we prove a nontrivial estimate of the form Σn≤x Λ(n)χ(n − l) ≪xexp{−0.6lnD}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \ll x\exp \{ - 0.6\sqrt {\ln D} \} $$\end{document} for the sum of values of χ over a sequence of shifted primes in the case when x ≥ D1/2+ε, (l,D) = 1, and the modulus of the primitive character generated by χ is a cube-free number.