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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
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
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
Linking options:
https://www.mathnet.ru/eng/im1328https://doi.org/10.1070/IM1988v031n02ABEH001074 https://www.mathnet.ru/eng/im/v51/i5/p994
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Abstract page: | 557 | Russian version PDF: | 229 | English version PDF: | 8 | References: | 52 | First page: | 1 |
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