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Chebyshevskii Sb., 2019, Volume 20, Issue 4, Pages 281–305 (Mi cheb849)  

Short cubic exponential sums with Möbius function

Z. Kh. Rakhmonov, F. Z. Rahmonov

Dzhuraev Institute of Mathematics, Academy of Sciences of Republic of Tajikistan, Dushanbe

Abstract: The work is dedicated to the conclusion of non-trivial estimates of short cubic exponential sums with Möbius function of the form
$$ S_3(\alpha;x,y) = \sum_{x-y<n\le x} \mu(n) e(\alpha n^3), $$
over minor arcs $\mathfrak{m}(\mathscr L^{32(B+18)})$ for $y\ge x^\frac{4}{5}\mathscr L^{8B+944}$ and $\tau=y^5x^{-2}\mathscr L^{-32(B+18)}.$

Keywords: shorts double exponential sum, Möbius function, method for estimating exponential sums with prime numbers, nontrivial estimate, minor arcs.

DOI: https://doi.org/10.22405/2226-8383-2018-20-4-281-305

Full text: PDF file (753 kB)
References: PDF file   HTML file

UDC: 511.32
Received: 15.11.2019
Accepted:20.12.2019

Citation: Z. Kh. Rakhmonov, F. Z. Rahmonov, “Short cubic exponential sums with Möbius function”, Chebyshevskii Sb., 20:4 (2019), 281–305

Citation in format AMSBIB
\Bibitem{RakRah19}
\by Z.~Kh.~Rakhmonov, F.~Z.~Rahmonov
\paper Short cubic exponential sums with Möbius function
\jour Chebyshevskii Sb.
\yr 2019
\vol 20
\issue 4
\pages 281--305
\mathnet{http://mi.mathnet.ru/cheb849}
\crossref{https://doi.org/10.22405/2226-8383-2018-20-4-281-305}


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