Sums of values of non-principal characters over shifted primes

TL;DR

This paper establishes a nontrivial estimate for sums of non-principal character values over shifted primes, extending understanding of character sums in analytic number theory for large moduli.

Contribution

It provides a new bound for sums of non-principal characters over shifted primes when the shift and modulus satisfy certain size conditions.

Findings

The estimate holds for $x \\ge D^{5/6+\\varepsilon}$ with coprime $(l,D)$.

The sum is bounded by $x \\exp(-0.6\sqrt{\\ln D})$, showing exponential decay.

The result advances bounds on character sums over primes in shifted sequences.

Abstract

For a nonprincipal character $\chi$ modulo $D$, when $x\ge D^{\frac56+\varepsilon}$, $(l,D) = 1$, 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.