It is established that all even positive integers up to N but at most O（N15/16＋ε） exceptions can be expressed in the form p1^2＋ p2^3＋ p3^4＋ p4^5,where p1,p2,p3 and p4 are prime numbers.
We prove that,with at most O(N17/192+ε)exceptions,all even positive integers up to N are expressible in the form P1^2+P2^2+P3^3+P5^4+P6^4,where Pi,P2,……,P6 are prime numbers.This gives large improvement of a recent...We prove that,with at most O(N17/192+ε)exceptions,all even positive integers up to N are expressible in the form P1^2+P2^2+P3^3+P5^4+P6^4,where Pi,P2,……,P6 are prime numbers.This gives large improvement of a recent result 0(N13/16+ε)due to M.Zhang and J.J.Li.展开更多
We consider exceptional sets in the Waring-Goldbach problem for fifth powers.For example,we prove that all but O(N^(131/132))integers satisfying the necessary local conditions can be represented as the sum of 11 fifth...We consider exceptional sets in the Waring-Goldbach problem for fifth powers.For example,we prove that all but O(N^(131/132))integers satisfying the necessary local conditions can be represented as the sum of 11 fifth powers of primes,which improves the previous results due to A.V.Kumchev[Canad.J.Math.,2005,57:298–327]and Z.X.Liu[Int.J.Number Theory,2012,8:1247–1256].展开更多
In this paper, it is proved that with at most O（N65/66） exceptions, all even positive integers up to N are expressible in the form p^2 2＋p^3 3＋p^4 4＋p^5 5. This improves a recent result O（N19193/19200＋ε） due...In this paper, it is proved that with at most O（N65/66） exceptions, all even positive integers up to N are expressible in the form p^2 2＋p^3 3＋p^4 4＋p^5 5. This improves a recent result O（N19193/19200＋ε） due to C. Bauer.展开更多
基金Supported by National Natural Science Foundation of China(Grant No.11326205)
文摘It is established that all even positive integers up to N but at most O（N15/16＋ε） exceptions can be expressed in the form p1^2＋ p2^3＋ p3^4＋ p4^5,where p1,p2,p3 and p4 are prime numbers.
基金The author would like to express the most sincere gratitude to Prof.Zhixin Liu for his valuable advice and constant encouragementThis work was supported by the National Natural Science Foundation of China(Grant No.11871367).
文摘We prove that,with at most O(N17/192+ε)exceptions,all even positive integers up to N are expressible in the form P1^2+P2^2+P3^3+P5^4+P6^4,where Pi,P2,……,P6 are prime numbers.This gives large improvement of a recent result 0(N13/16+ε)due to M.Zhang and J.J.Li.
基金The first author was supported by the Scientific Research Project of the Education Department of Fujian Province(Grant No.JAT190370)the Natural Science Foundation of Fujian Province(Grant No.2020J05162)+1 种基金The second author was supported by the National Natural Science Foundation of China(Grant No.11871367)the Natural Science Foundation of Tianjin City(Grant No.19JCQNJC14200).
文摘We consider exceptional sets in the Waring-Goldbach problem for fifth powers.For example,we prove that all but O(N^(131/132))integers satisfying the necessary local conditions can be represented as the sum of 11 fifth powers of primes,which improves the previous results due to A.V.Kumchev[Canad.J.Math.,2005,57:298–327]and Z.X.Liu[Int.J.Number Theory,2012,8:1247–1256].
基金Supported by Post-Doctoral Fellowship of The University of Hong KongThe National Natural Science Foundation(Grant No.10571107)Supported by a grant from the Research Grant Council of Hong Kong(Project No.HKU7028/03P)
文摘In this paper, it is proved that with at most O（N65/66） exceptions, all even positive integers up to N are expressible in the form p^2 2＋p^3 3＋p^4 4＋p^5 5. This improves a recent result O（N19193/19200＋ε） due to C. Bauer.
