On the Waring-Goldbach Problem for Six Cubes and Two Biquadrates

被引：0
作者：
Shi, Sanying [1 ]
Liu, Li [1 ]
机构：
[1] Hefei Univ Technol, Sch Math, Hefei 230009, Anhui, Peoples R China
来源：
CHINESE ANNALS OF MATHEMATICS SERIES B | 2018年 / 39卷 / 06期
基金：
中国国家自然科学基金;
关键词：
Waring-Goldbach problem; Hardy-Littlewood method; Sieve theory; SUMS;
D O I：
10.1007/s11401-018-0112-6
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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.
引用
收藏
页码：1033 / 1046
页数：14
相关论文
共 13 条
[1]  
BRUDERN J, 1995, ANN SCI ECOLE NORM S, V28, P461
[2]  
BRUDERN J, 1988, J LOND MATH SOC, V37, P25
[3]  
Brudern J., 1991, Mathematica Gottingenis, V51
[4]   Waring-Goldbach problem: two squares and some unlike powers [J].
Cai, Y. C. ;
Mu, Q. W. .
ACTA MATHEMATICA HUNGARICA, 2015, 145 (01) :46-67
[5]   The Waring-Goldbach problem: one square and five cubes [J].
Cai, Yingchun .
RAMANUJAN JOURNAL, 2014, 34 (01) :57-72
[6]  
Halberstam H., 1974, Lond. Math. Soc. Monographs
[7]   ON WARING PROBLEM [J].
HOOLEY, C .
ACTA MATHEMATICA, 1986, 157 (1-2) :49-97
[8]  
Hua, 1965, ADDITIVE THEORY PRIM
[9]  
Iwaniec H., 1980, Acta Arith, V37, P307, DOI DOI 10.4064/AA-37-1-307-320
[10]  
Titchmarsh EG., 1986, THEORY RIEMANN ZETA
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