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| On the Waring-Goldbach Problem for Six Cubes and Two Biquadrates |
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Citation： |
Sanying SHI,Li LIU.On the Waring-Goldbach Problem for Six Cubes and Two Biquadrates[J].Chinese Annals of Mathematics B,2018,39(6):1033~1046 |
| Page view： 662
Net amount： 759 |
Authors： |
Sanying SHI; Li LIU |
Foundation： |
This work was supported by the National Natural Science
Foundation of China (No.11201107) and the China Scholarship
Council. |
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| Abstract： |
Let $P_r$ denote an almost prime with at most $r$ prime factors,
counted according to multiplicity. In the present paper, it is
proved that for any sufficiently large even integer $n$, the
equation
$$ n=x^3+p_1^3+p_2^3+p_3^3+p_4^3+p_5^3+p_6^4+p_7^4$$ has solutions
in primes $p_i$ with $x$ being a $P_6$. This result constitutes a
refinement upon that of Hooley C. |
Keywords： |
Waring-Goldbach problem, Hardy-Littlewood method, Sieve theory |
Classification： |
11P32, 11N36 |
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