Sums of values of non-principal characters over shifted primes

Abstract

For a nonprincipal character $\chi$ modulo $D$, when $x\ge D^{\frac{5}{6}+\epsilon }$, $(l,D)=1$, we prove a nontrivial estimate of the form ${\sum }_{n\le x}\Lambda (n)\chi (n-l)\ll x\exp \left(-0.6\sqrt{\ln D}\right)$ for the sum of values of $\chi$ over a sequence of shifted primes. Bibliography: 41 references.

This is an updated version of the paper published under the same title in 2018. Refer to the DOI provided below

Cited by in corpus (1)

• Distribution of products of shifted primes in arithmetic progressions with increasing difference