ζk is one of the most important constant in the siève methods.Tlus paper gives the relatively accurate lower bound and upper bound on it,that is,3<sup>-1/k</sup>ck,where c=1.22... and k】16.
Using the circle method and sieves, the author proves that a positive proportion of positive integers can be represented as the sum of four cubes of primes.
It is proved that for almost all sufficiently large even integers n, the prime variable equation n = p1 ＋ p2, p1 ∈ Pγ is solvable, with 13/15 〈γ≤ 1, where Pγ = {p ｜p = [m^1/γ], for integer m and prime p} is t...It is proved that for almost all sufficiently large even integers n, the prime variable equation n = p1 ＋ p2, p1 ∈ Pγ is solvable, with 13/15 〈γ≤ 1, where Pγ = {p ｜p = [m^1/γ], for integer m and prime p} is the set of the Piatetski-Shapiro primes.展开更多
Under the Generalized Riemann Hypothesis, it is proved that for any integer \%k≥770\% there is \%N\-k>0\% depending on \%k\% only such that every even integer ≥\%N\-k\% is a sum of two odd prime numbers and \%k\...Under the Generalized Riemann Hypothesis, it is proved that for any integer \%k≥770\% there is \%N\-k>0\% depending on \%k\% only such that every even integer ≥\%N\-k\% is a sum of two odd prime numbers and \%k\% powers of 2.展开更多
Let l1,l2,…,lg be even integers and x be a sufficiently large number.In this paper,the authors prove that the number of positive odd integers k≤x such that（k+l1）2,（k+l2）2,…,（k+lg）2 can not be expressed as 2n+...Let l1,l2,…,lg be even integers and x be a sufficiently large number.In this paper,the authors prove that the number of positive odd integers k≤x such that（k+l1）2,（k+l2）2,…,（k+lg）2 can not be expressed as 2n+pαis at least c（g）x,where p is an odd prime and the constant c（g）depends only on g.展开更多
Let N be a sufficiently large even integer.Let p denote a prime and P2 denote an almost prime with at most two prime factors.In this paper,it is proved that the equation N = p + P2(p ≤ N0.945) is solvable.
文摘ζk is one of the most important constant in the siève methods.Tlus paper gives the relatively accurate lower bound and upper bound on it,that is,3<sup>-1/k</sup>ck,where c=1.22... and k】16.
基金Project supported by the National Natural Science Foundation of China (No.10041004) and the ThansCentury naming Programme Foun
文摘Using the circle method and sieves, the author proves that a positive proportion of positive integers can be represented as the sum of four cubes of primes.
基金Project supported by the Foundation of Shandong Provincial Education Department in China (No.03F06)the Grant for Doctoral Fellows in Shandong Finance Institute
文摘It is proved that for almost all sufficiently large even integers n, the prime variable equation n = p1 ＋ p2, p1 ∈ Pγ is solvable, with 13/15 〈γ≤ 1, where Pγ = {p ｜p = [m^1/γ], for integer m and prime p} is the set of the Piatetski-Shapiro primes.
基金ProjectpartiallysupportedbyRGCResearchGrant (No .HKU 712 2 / 97P)andPost DoctoralFellowshipoftheUniversityofHongKong .
文摘Under the Generalized Riemann Hypothesis, it is proved that for any integer \%k≥770\% there is \%N\-k>0\% depending on \%k\% only such that every even integer ≥\%N\-k\% is a sum of two odd prime numbers and \%k\% powers of 2.
基金supported by the National Natural Science Foundation of China(Nos.10771103,10801075)the Natural Science Foundation of Huaihai Institute of Technology(No.KQ10002)
文摘Let l1,l2,…,lg be even integers and x be a sufficiently large number.In this paper,the authors prove that the number of positive odd integers k≤x such that（k+l1）2,（k+l2）2,…,（k+lg）2 can not be expressed as 2n+pαis at least c（g）x,where p is an odd prime and the constant c（g）depends only on g.
基金Project supported by the National Natural Science Foundation of China(No.11071186)the Science Foundation for the Excellent Youth Scholars of Shanghai(No.ssc08017)the Doctoral Research Fund of Shanghai Ocean University
文摘Let N be a sufficiently large even integer.Let p denote a prime and P2 denote an almost prime with at most two prime factors.In this paper,it is proved that the equation N = p + P2(p ≤ N0.945) is solvable.
