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Chebyshevskii Sb., 2008, Volume 9, Issue 1, Pages 4–8 (Mi cheb123)  

On the Goldba˝h-numbers

I. A. Allakov

Termez State University

Abstract: 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 $E(N)<N^{1-\delta}$ values of $n$. Here $N$ is sufficiently large natural number, $p_1$, $p_2$, $p_3$ — are prime numbers, $\delta$ ($0<\delta<1$) is small positive constant. In prove used of Generalized Rieman Hypothesis.

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Bibliographic databases:
UDC: 511.3
MSC: 11P32
Received: 15.09.2008

Citation: I. A. Allakov, “On the Goldba˝h-numbers”, Chebyshevskii Sb., 9:1 (2008), 4–8

Citation in format AMSBIB
\Bibitem{All08}
\by I.~A.~Allakov
\paper On the Goldba˝h-numbers
\jour Chebyshevskii Sb.
\yr 2008
\vol 9
\issue 1
\pages 4--8
\mathnet{http://mi.mathnet.ru/cheb123}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2894375}


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