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

Abstract

For a nonprincipal character χ modulo D, we prove a nontrivial estimate of the form Σ_n≤x Λ(n)χ(n − l) \( \ll x\exp \{ - 0.6\sqrt {\ln D} \} \) for the sum of values of χ over a sequence of shifted primes in the case when x ≥ D^1/2+ε, (l,D) = 1, and the modulus of the primitive character generated by χ is a cube-free number.