Geodesic
Short cubic exponential sums with Möbius function
Čebyševskij sbornik, Tome 20 (2019) no. 4, pp. 281-305

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The work is dedicated to the conclusion of non-trivial estimates of short cubic exponential sums with Möbius function of the form $$ S_3(\alpha;x,y) = \sum_{x-y\le x} \mu(n) e(\alpha n^3), $$ 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. 
@article{CHEB_2019_20_4_a18,
     author = {Z. Kh. Rakhmonov and F. Z. Rahmonov},
     title = {Short cubic exponential sums with {M\"obius} function},
     journal = {\v{C}eby\v{s}evskij sbornik},
     pages = {281--305},
     publisher = {mathdoc},
     volume = {20},
     number = {4},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2019_20_4_a18/}
}
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Z. Kh. Rakhmonov; F. Z. Rahmonov. Short cubic exponential sums with Möbius function. Čebyševskij sbornik, Tome 20 (2019) no. 4, pp. 281-305. http://geodesic.mathdoc.fr/item/CHEB_2019_20_4_a18/