Geodesic
About simultaneous representation of numbers by sum of primes
Čebyševskij sbornik, Tome 13 (2012) no. 2, pp. 12-17 
I. Allakov; A. Safarov. About simultaneous representation of numbers by sum of primes. Čebyševskij sbornik, Tome 13 (2012) no. 2, pp. 12-17. http://geodesic.mathdoc.fr/item/CHEB_2012_13_2_a2/
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     title = {About simultaneous representation of numbers by sum of primes},
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper proved theorem Theorema. If $X$ -it is enough big, $\delta$ ($0\delta1$) it is enough small real numbers, that fair estimation $$ J(\overrightarrow{b})>\frac{\Bigl(\frac{1}{\sqrt{n}}3(n!)^{2}B^{(2n-1)}|\overrightarrow{b}|\Bigr)^{1-\frac{\delta}{10(n-1)}}}{\Bigl(\ln\Bigl(\frac{1}{\sqrt{n}}3(n!)^{2}B^{(2n-1)}|\overrightarrow{b}|\Bigr)\Bigr)^{n+1}}, $$ for all vector $\overrightarrow{b}\in U(X)$ with the exclusion of no more than $$ E(X)^{n-\frac{\delta}{17n^{3}}} $$ the vector of them. Here $B=\max\{3|a_{ij}|\}$, $1\leq i \leq n$, $1\leq j \leq n+1$.

[1] Wu Fang, “On the solutions of the systems of linear equations with prime variables”, Acta Math. Sinica, 1957, no. 7, 102–121

[2] Babanazarov B., Tulaganova M. I., Fainleib A. S., Dokl. AN RUz., 1992, no. 6–7, 7–9

[3] Allakov I., Israilov M. I., Dokl. AN RUz., 1992, no. 10–11, 12–15

[4] Liu M. C., Tsang K. M., “On pairs of linear equations in three prime variables and application to Goldbach's problem”, J. reine angew. Math., 1989, no. 399, 109–136 | MR | Zbl

[5] Allakov I., Abraev B., “O kolichestve reshenii pary lineinykh uravnenii s tremya prostymi peremennymi”, Algebra i teoriya chisel: sovremennye problemy i prilozheniya, tezisy dokladov VIII Mezhdunarodnoi konferentsii, 4–5 | Zbl

[6] Allakov I., Issledovanie plotnosti chislovykh posledovatelnostei analiticheskimi metodami, Dissertatsiya na soiskanie uchenoi stepeni d.f.-m.n., Institut matematiki i informatsionnykh tekhnologii AN RUz., T., 2008

[7] Karatsuba A. A., Osnovy analiticheskoi teorii chisel, Nauka, M., 1983, 240 pp. | MR