Geodesic
Waring's problem in natural numbers of special form
Sbornik. Mathematics, Tome 211 (2020) no. 5, pp. 733-749

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Let $\mathbb N_0$ be the set of positive integers whose binary decompositions contain an even number of ones. We give a bound for the trigonometric sum of special form over numbers in $\mathbb N_0$; using this bound, we derive an asymptotic formula for the number of solutions to Waring's equation in positive integers in $\mathbb N_0$, and also a bound for the number of terms in the last equation, which is sufficient for the equation to be solvable in integers in $\mathbb N_0$. Bibliography: 9 titles.
Keywords: Waring's problem, circle method, trigonometric sums. 
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     author = {K. M. Eminyan},
     title = {Waring's problem in natural numbers of special form},
     journal = {Sbornik. Mathematics},
     pages = {733--749},
     publisher = {mathdoc},
     volume = {211},
     number = {5},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2020_211_5_a4/}
}
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K. M. Eminyan. Waring's problem in natural numbers of special form. Sbornik. Mathematics, Tome 211 (2020) no. 5, pp. 733-749. http://geodesic.mathdoc.fr/item/SM_2020_211_5_a4/