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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2017, Volume 296, Pages 220–242
DOI: https://doi.org/10.1134/S0371968517010174
(Mi tm3774)
 

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

Short cubic exponential sums over primes

Z. Kh. Rakhmonov, F. Z. Rahmonov

Mathematics Institute and Computing Center, Academy of Sciences of the Republic of Tadzhikistan
Full-text PDF (291 kB) Citations (3)
References:
Abstract: For $y\ge x^{4/5}\mathscr L^{8B+151}$ (where $\mathscr L=\log (xq)$ and $B$ is an absolute constant), a nontrivial estimate is obtained for short cubic exponential sums over primes of the form $S_3(\alpha ;x,y) = \sum _{x-y<n\le x}\Lambda (n) e(\alpha n^3)$, where $\alpha =a/q+\theta /q^2$, $(a,q)=1$, $\mathscr L^{32(B+20)}<q\le y^5x^{-2}\mathscr L^{-32(B+20)}$, $|\theta |\le 1$, $\Lambda $ is the von Mangoldt function, and $e(t)=e^{2\pi it}$.
Received: May 6, 2016
English version:
Proceedings of the Steklov Institute of Mathematics, 2017, Volume 296, Pages 211–233
DOI: https://doi.org/10.1134/S0081543817010175
Bibliographic databases:
Document Type: Article
UDC: 511.325
Language: Russian
Citation: Z. Kh. Rakhmonov, F. Z. Rahmonov, “Short cubic exponential sums over primes”, Analytic and combinatorial number theory, Collected papers. On the occasion of the 125th anniversary of the birth of Academician Ivan Matveevich Vinogradov, Trudy Mat. Inst. Steklova, 296, MAIK Nauka/Interperiodica, Moscow, 2017, 220–242; Proc. Steklov Inst. Math., 296 (2017), 211–233
Citation in format AMSBIB
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\paper Short cubic exponential sums over primes
\inbook Analytic and combinatorial number theory
\bookinfo Collected papers. On the occasion of the 125th anniversary of the birth of Academician Ivan Matveevich Vinogradov
\serial Trudy Mat. Inst. Steklova
\yr 2017
\vol 296
\pages 220--242
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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  • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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