Abstract
For a nonprincipal character χ modulo D, we prove a nontrivial estimate of the form Σn≤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 ≥ D1/2+e, (l,D) = 1, and the modulus of the primitive character generated by χ is a cube-free number.
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