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Izv. Akad. Nauk SSSR Ser. Mat., 1987, Volume 51, Issue 5, Pages 994–1009 (Mi izv1328)  

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

The distribution of pairs of quadratic residues and nonresidues of a special form

A. A. Karatsuba


Abstract: Nontrivial estimates are obtained for sums of Legendre symbols of a quadratic polynomial over primes in an arithmetic progression. These estimates are used to prove a theorem concerning the number of pairs of the form $(p+a,p+b)$, $p\equiv l(\operatorname{mod}k)$, $p\leqslant N$, for which $p+a$ is a quadratic residue (nonresidue), $p+b$ is a quadratic residue (nonresidue) modulo the prime $q$, and $N>k^3q^{0.75+\varepsilon}$.
Bibliography: 27 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1988, 31:2, 307–323

Bibliographic databases:

UDC: 511
MSC: Primary 11L20, 11L40; Secondary 11L03, 11L26, 11M26
Received: 22.05.1986

Citation: A. A. Karatsuba, “The distribution of pairs of quadratic residues and nonresidues of a special form”, Izv. Akad. Nauk SSSR Ser. Mat., 51:5 (1987), 994–1009; Math. USSR-Izv., 31:2 (1988), 307–323

Citation in format AMSBIB
\Bibitem{Kar87}
\by A.~A.~Karatsuba
\paper The distribution of pairs of quadratic residues and nonresidues of a~special form
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1987
\vol 51
\issue 5
\pages 994--1009
\mathnet{http://mi.mathnet.ru/izv1328}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=925091}
\zmath{https://zbmath.org/?q=an:0679.10031|0637.10025}
\transl
\jour Math. USSR-Izv.
\yr 1988
\vol 31
\issue 2
\pages 307--323
\crossref{https://doi.org/10.1070/IM1988v031n02ABEH001074}


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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. G. D. Negmatova, “The distribution of values of non-principal characters in lacunary sequences”, Russian Math. Surveys, 44:5 (1989), 214–215  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. A. A. Karatsuba, “Arithmetic problems in the theory of Dirichlet characters”, Russian Math. Surveys, 63:4 (2008), 641–690  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    3. M. A. Korolev, “On Anatolii Alekseevich Karatsuba's works written in the 1990s and 2000s”, Proc. Steklov Inst. Math., 299 (2017), 1–43  mathnet  crossref  crossref  isi  elib  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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