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Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 2013, Volume 13, Issue 4(2), Pages 113–117 (Mi isu469)  

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

Mathematics

Distribution of values of Dirichlet characters in the sequence of shifted primes

Z. Kh. Rakhmonov

Institute ofMathematics, Academy of Sciences of the Republic of Tajikistan, 734063, Dushanbe, Ayni st., 83

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.

DOI: https://doi.org/10.18500/1816-9791-2013-13-4-113-117

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UDC: 511.325

Citation: Z. Kh. Rakhmonov, “Distribution of values of Dirichlet characters in the sequence of shifted primes”, Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 13:4(2) (2013), 113–117

Citation in format AMSBIB
\Bibitem{Rak13}
\by Z.~Kh.~Rakhmonov
\paper Distribution of values of Dirichlet characters in the sequence of shifted primes
\jour Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform.
\yr 2013
\vol 13
\issue 4(2)
\pages 113--117
\mathnet{http://mi.mathnet.ru/isu469}
\crossref{https://doi.org/10.18500/1816-9791-2013-13-4-113-117}
\elib{http://elibrary.ru/item.asp?id=21976915}


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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, “Summy kharakterov s prostymi chislami”, Chebyshevskii sb., 15:2 (2014), 73–100  mathnet
    2. 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
    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
  • Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика
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