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| A Hybrid of Theorems of Goldbach and Piatetski-Shapiro |
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Citation： |
Xianmeng MENG,Mingqiang WANG.A Hybrid of Theorems of Goldbach and Piatetski-Shapiro[J].Chinese Annals of Mathematics B,2006,27(3):341~352 |
| Page view： 1069
Net amount： 811 |
Authors： |
Xianmeng MENG; Mingqiang WANG |
Foundation： |
Project supported by the Foundation of Shandong Provincial Education Department in China (No.03F06)
and the Grant for Doctoral Fellows in Shandong Finance Institute. |
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| Abstract： |
It is proved that for almost all sufficiently large even integers
$n$, the prime variable equation $n=p_1+p_2$, $p_1\in P_{\gamma}$ is solvable, with $13/15<\gamma\leq 1$,
where $P_{\gamma}=\{p\mid p=[m^{\frac{1}{\gamma}}], \mbox{ for integer } m \mbox{ and prime }p\}$
is the set of the Piatetski-Shapiro primes. |
Keywords： |
Circle method, Sieve method, Goldbach problem |
Classification： |
11P32, 11P55 |
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