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Chebyshevskii Sb., 2014, Volume 15, Issue 2, Pages 73–100 (Mi cheb342)  

This article is cited in 3 scientific papers (total in 3 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.

Full text: PDF file (297 kB)
References: PDF file   HTML file
UDC: 511.524
Received: 24.04.2014

Citation: Z. Kh. Rakhmonov, “Sums of characters over prime numbers”, Chebyshevskii Sb., 15:2 (2014), 73–100

Citation in format AMSBIB
\Bibitem{Rak14}
\by Z.~Kh.~Rakhmonov
\paper Sums of characters over prime numbers
\jour Chebyshevskii Sb.
\yr 2014
\vol 15
\issue 2
\pages 73--100
\mathnet{http://mi.mathnet.ru/cheb342}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Z. Kh. Rakhmonov, Sh. Kh. Mirzorakhimov, “Summy kharakterov po modulyu svobodnogo ot kubov na sdvinutykh prostykh”, Chebyshevskii sb., 17:1 (2016), 201–216  mathnet  elib
    2. Z. Kh. Rakhmonov, F. Z. Rahmonov, “Short cubic exponential sums over primes”, Proc. Steklov Inst. Math., 296 (2017), 211–233  mathnet  crossref  crossref  mathscinet  isi  elib
    3. Z. Kh. Rakhmonov, “Sums of values of nonprincipal characters over a sequence of shifted primes”, Proc. Steklov Inst. Math., 299 (2017), 219–245  mathnet  crossref  crossref  isi  elib
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