Two results on powers of two in Waring-Goldbach type problems

被引：5

作者：

Liu, Huafeng ^{[1
]}

机构：

[1] Shandong Univ, Sch Math, Jinan 250100, Shandong, Peoples R China

来源：

INTERNATIONAL JOURNAL OF NUMBER THEORY | 2016年 / 12卷 / 07期

关键词：

The Hardy-Littlewood method; Waring-Goldbach problem; powers of two; ONE PRIME; ODD INTEGERS; SQUARES; SUM; REPRESENTATION; CONJECTURE;

D O I：

10.1142/S1793042116501128

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, it is proved that for k = 31, every sufficient large odd integer is a sum of one prime, two squares of primes and k powers of two. Furthermore, for k' = 116, every pair of large odd integers satisfying some necessary conditions can be represented in the form of a pair of one prime, two squares of primes and k' powers of two. These improve the previous results k = 35 and k' = 332.

引用

页码：1813 / 1825

页数：13

共 17 条

[1] [Anonymous], 2006, THESIS
[2] Some problems of 'partitio numerorum', III On the expression of a number as a sum of primes
Hardy, GH
Littlewood, JE
[J]. ACTA MATHEMATICA, 1923, 44 (01) : 1 - 70
[3] Heath-Brown D. R., 2002, ASIAN J MATH, V6, P535, DOI DOI 10.4310/AJM.2002.V6.N3.A7
[4] Hua LK., 1938, Quart. J. Math. Oxford, V9, P68, DOI [10.1093/qmath/os-9.1.68, DOI 10.1093/QMATH/OS-9.1.68]
[5] Representation of odd integers as the sum of one prime, two squares of primes and powers of 2
Li, Hongze
[J]. ACTA ARITHMETICA, 2007, 128 (03) : 223 - 233
[6] LINNIK IV, 1959, DOKL AKAD NAUK SSSR+, V124, P29
[7] Linnik Y., 1960, DOKL AKAD NAUK SSSR, V24, P629
[8] Four squares of primes and 165 powers of 2
Liu, JY
Lu, GS
[J]. ACTA ARITHMETICA, 2004, 114 (01) : 55 - 70
[9] Squares of primes and powers of 2
Liu, JY
Liu, MC
Zhan, T
[J]. MONATSHEFTE FUR MATHEMATIK, 1999, 128 (04): : 283 - 313
[10] Representation of odd integers as the sum of one prime, two squares of primes and powers of 2
Liu, T
[J]. ACTA ARITHMETICA, 2004, 115 (02) : 97 - 118

← 1 2 →