Geodesic
Sums of characters over prime numbers
Čebyševskij sbornik, Tome 15 (2014) no. 2, pp. 73-100

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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. 
@article{CHEB_2014_15_2_a5,
     author = {Z. Kh. Rakhmonov},
     title = {Sums of characters over prime numbers},
     journal = {\v{C}eby\v{s}evskij sbornik},
     pages = {73--100},
     publisher = {mathdoc},
     volume = {15},
     number = {2},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2014_15_2_a5/}
}
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Z. Kh. Rakhmonov. Sums of characters over prime numbers. Čebyševskij sbornik, Tome 15 (2014) no. 2, pp. 73-100. http://geodesic.mathdoc.fr/item/CHEB_2014_15_2_a5/