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Chebyshevskii Sbornik, 2019, Volume 20, Issue 2, Pages 336–347
DOI: https://doi.org/10.22405/2226-8383-2018-20-2-336-347
(Mi cheb774)
 

The mean value of products of Legendre symbol over primes

V. N. Chubarikov

Mechanics and Mathematics Faculty, Moscow State University named after M. V. Lomonosov (Moscow)
References:
Abstract: In the paper the asymptotical formula as $N\to\infty$ for the number of primes $p\leq N,$ satisfying to the system of equations
$$ \left(\frac{p+k_s}{q_s}\right)=\vartheta_s, s=1,\dots ,r, $$
where $q_1,\dots ,q_r$ — different primes, $\vartheta_s$ may be take only two values $+1$ or $-1,$ but natural numbers $k_s$ take noncongruent values on modulus $q_s, s=1,\dots ,r,$ i.e. $k_s\not\equiv k_t\pmod{q_s}, t=1,\dots ,r,$ is found.
The finding asymptotics is nontrivial as $q=q_1\dots q_r\gg N^{1+\varepsilon},$ moreover the number of $r$ may grow up as $o(\ln N).$ Here $\varepsilon>0$ is an arbitrary constant.
Keywords: the Legendre symbol, the Vinogradov method of estimating on sums over primes, the Dirichlet's character, the Vinogradov's combinatorial sieve, the method of double sums.
Received: 19.05.2019
Accepted: 12.07.2019
Document Type: Article
UDC: 511.3
Language: Russian
Citation: V. N. Chubarikov, “The mean value of products of Legendre symbol over primes”, Chebyshevskii Sb., 20:2 (2019), 336–347
Citation in format AMSBIB
\Bibitem{Chu19}
\by V.~N.~Chubarikov
\paper The mean value of products of Legendre symbol over primes
\jour Chebyshevskii Sb.
\yr 2019
\vol 20
\issue 2
\pages 336--347
\mathnet{http://mi.mathnet.ru/cheb774}
\crossref{https://doi.org/10.22405/2226-8383-2018-20-2-336-347}
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