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Chebyshevskii Sb., 2012, Volume 13, Issue 2, Pages 12–17 (Mi cheb30)  

About simultaneous representation of numbers by sum of primes

I. Allakov, A. Safarov

Termez State University

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

Full text: PDF file (362 kB)
References: PDF file   HTML file
UDC: 511.28
Received: 21.04.2012

Citation: I. Allakov, A. Safarov, “About simultaneous representation of numbers by sum of primes”, Chebyshevskii Sb., 13:2 (2012), 12–17

Citation in format AMSBIB
\Bibitem{AllSaf12}
\by I.~Allakov, A.~Safarov
\paper About simultaneous representation of numbers by sum of primes
\jour Chebyshevskii Sb.
\yr 2012
\vol 13
\issue 2
\pages 12--17
\mathnet{http://mi.mathnet.ru/cheb30}


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