Geodesic
On the Goldbaсh-numbers
Čebyševskij sbornik, Tome 9 (2008) no. 1, pp. 4-8 
I. A. Allakov. On the Goldbaсh-numbers. Čebyševskij sbornik, Tome 9 (2008) no. 1, pp. 4-8. http://geodesic.mathdoc.fr/item/CHEB_2008_9_1_a0/
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     title = {On the {Goldba{\cyrs}h-numbers}},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2008_9_1_a0/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper proved asymptotic formula $$ R(n)=\sum\limits_{n=p_1+p_2}\ln p_1\ln p_2=2n\prod\limits_{p>2}\frac{p(p-2)}{(p-1)^2}\prod\limits_{\genfrac{}{}{0pt}{}{p\setminus n}{ p>2}}\frac{p-1}{p-2}+O(n^{1-2\delta}) $$ for all even $n\leq N,$ with the exception can of at most $E(N)$ values of $n$. Here $N$ is sufficiently large natural number, $p_1$, $p_2$, $p_3$ — are prime numbers, $\delta$ ($0\delta1$) is small positive constant. In prove used of Generalized Rieman Hypothesis.

[1] Lavrik A. F., “K binarnym problemam additivnoi teorii prostykh chisel v svyazi s metodom trigonometricheskikh summ I. M. Vinogradova”, Vestnik LGU, 13 (1961), 11–27 | MR

[2] Allakov I., “Nekotorye otsenki snizu dlya chisla predstavlenii goldbakhovykh chisel”, Vopr. vychisl. i prikl. matem., 77, RISO AN RUz., 1985, 37–42

[3] Allakov I., “O predstavlenii chisel summoi dvukh prostykh chisel iz arifmeticheskoi progresii”, Izv. VUZov “Matematika”, 2000, no. 8 (459), 3–15 | MR

[4] Montgomery H. L., Vaughan R. C., “The exceptional set in Goldbach's problem”, Acta arithm., 27 (1975), 353–370 | MR

[5] Allakov I., “Ob isklyuchitelnom mnozhestve v binarnoi probleme Goldbakha”, Izv. AN RUz.; Деп. в ВИНИТИ. Деп. No5166-81; РЖМат, 1982, 3А111, 76

[6] Allakov I., “Opredelenie konstant v modifitsirovannom plotnostnom neravenstve Gallakhera”, Vopr. vychisl. i prikl. matem., 62, RISO AN RUz., 1980, 42–56

[7] Lavrik A. F., “Nuli dzeta-funktsii Rimana”, Dokl. AN RUz., 2 (2005), 3–4