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| Waring-Goldbach Problem for Unlike Powers |
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Citation： |
Zhenzhen FENG,Jing MA.Waring-Goldbach Problem for Unlike Powers[J].Chinese Annals of Mathematics B,2025,46(2):303~320 |
| Page view： 466
Net amount： 244 |
Authors： |
Zhenzhen FENG; Jing MA |
Foundation： |
the National Natural Science Foundation of China (No. 11771252) and the
Natural Science Foundation of Fujian Province (Nos. 2024J01805, 2022J02046). |
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| Abstract： |
In this paper, the authors investigate exceptional sets in the Waring-Goldbach
problem for unlike powers. For example, estimates are obtained for sufficiently large integers below a parameter subject to the necessary local conditions that do not have a
representation as the sum of a square of prime, a cube of prime and a sixth power of prime
and a k-th power of prime. These results improve the recent result due to Br¨udern in the
order of magnitude. Furthermore, the method can be also applied to the similar estimates
for the exceptional sets for Waring-Goldbach problem for unlike powers. |
Keywords： |
Exceptional sets Waring-Goldbach problem Circle method |
Classification： |
11P32, 11P55 |
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