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Mathematics of the USSR-Izvestiya, 1988, Volume 31, Issue 2, Pages 307–323
DOI: https://doi.org/10.1070/IM1988v031n02ABEH001074
(Mi im1328)
 

This article is cited in 4 scientific papers (total in 4 papers)

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

A. A. Karatsuba
References:
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.
Received: 22.05.1986
Russian version:
Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya, 1987, Volume 51, Issue 5, Pages 994–1009
Bibliographic databases:
Document Type: Article
UDC: 511
MSC: Primary 11L20, 11L40; Secondary 11L03, 11L26, 11M26
Language: English
Original paper language: Russian
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/im1328}
\mathscinet{http://mathscinet.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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  • https://www.mathnet.ru/eng/im1328
  • https://doi.org/10.1070/IM1988v031n02ABEH001074
  • https://www.mathnet.ru/eng/im/v51/i5/p994
  • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
    Statistics & downloads:
    Abstract page:557
    Russian version PDF:229
    English version PDF:8
    References:52
    First page:1
     
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