Character sums over shifted primes

Abstract

For integer $q$, let $\chi$ be a primitive multiplicative character$(\mathrm{mod}q).$ For integer $a$ coprime to $q$, we obtain a new bound for the sums $$\sum _{n\le N}\Lambda (n)\chi (n+a),$$ where $\Lambda (n)$ is the von Mangoldt function. This bound improves and extends the range of a result of Friedlander, Gong and Shparlinski

26 pages