This article is cited in 4 papers

Sums of characters over prime numbers

Z. Kh. Rakhmonov

Institute of Mathematics, Academy of Sciences of Republic of Tajikistan, Dushanbe

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^{\frac{5}{6}+\varepsilon}$ and refines the estimate obtained by J. B. Friedlander, K. Gong, I. E. Shparlinskii. Their estimate holds provided that $x\ge q^{\frac{8}{9}+\varepsilon}$.
Bibliography: 20 titles.

Keywords: Dirichlet character, shifted primes, short sums of characters, exponential sums over primes.

UDC: 511.524

Received: 24.04.2014