Abstract:
The new estimate for the sum of the values of a primitive Dirichlet character modulo an integer $q$ has been obtained over the sequence of shifted primes $p-l$, $(l,q)=1$, $p\le x$. This estimate is nontrivial for $x\ge q^{\frac56+\varepsilon}$ and refines the estimate obtained by J. B. Friedlander, K. Gong, I. E. Shparlinskii. Their estimate holds provided that $x\ge q^{8/9+\varepsilon}$.
Key words:Dirichlet character, shifted primes, short sums of characters, exponential sums over primes.