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  • 期刊=Frontiers of Mathematics in Chinax
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Waring−Goldbach problem for one prime power and four prime cubes under Riemann Hypothesis
《Frontiers of Mathematics in China》2023年第2期139-146,共8页Xiaoming PAN Liqun HU 
the National Natural Science Foundation of China(Grant No.11761048);the Natural Science Foundation of Jiangxi Province for Distinguished Young Scholars(Grant No.20212ACB211007);Natural Science Foundation of Jiangxi Province(Grant No.20224BAB201001).
Let k≥1 be an integer.Assume that RH holds.In this paper we prove that a suitable asymptotic formula for the average number of representations of integers n=p^(k)_(1)+p^(3)_(2)+p^(3)_(3)+p^(3)_(4)+p^(3)_(5),where p_(...
关键词：Hardy−Littlewood method Waring−Goldbach problem Riemann Hypothesis short intervals 
Matchings extend to Hamiltonian cycles in hyper cubes with faulty edges被引量：2
《Frontiers of Mathematics in China》2019年第6期1117-1132,共16页Xie-Bin CHEN 
The work was supported by the National Natural Science Foundation of China(Grant No.11401290).
We consider the problem of existence of a Hamiltonian cycle containing a matching and avoiding some edges in an n-cubc Qn,and obtain the following results.Let n≥3,MСE(Qn),and FСE(Qn)\M with 1≤|F|≤2n-4-|M|.If M is...
关键词：HYPERCUBE Hamiltonian cycle fault tolerance matching interconnection network 
Slim exceptional set for sums of two squares, two cubes, and two biquadrates of primes
《Frontiers of Mathematics in China》2019年第5期1017-1035,共19页Rui ZHANG 
The author would like to express the most sincere gratitude to Prof.Zhixin Liu for his valuable advice and constant encouragement;This work was supported by the National Natural Science Foundation of China(Grant No.11871367).
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...
关键词：Waring-Goldbach problem circle method exceptional set 
Sums of nine almost equal prime cubes被引量：1
《Frontiers of Mathematics in China》2014年第5期1131-1140,共10页Yanjun YAO 
We prove that each sufficiently large odd integer N can be written as sum of the form N = p1^3 ＋p2^3 ＋... ＋p9^3 with [pj - （N/9）^1/31 ≤ N^（1/3）-θ, where pj, j = 1,2,...,9, are primes and θ = （1/51） -ε.
关键词：Waring-Goldbach problem circle method exponential sum overprimes in short intervals 
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