On the Waring-Goldbach problem for seventh and higher powers

被引：19
|
作者：
Kumchev, Angel V. [1 ]
Wooley, Trevor D. [2 ]
机构：
[1] Towson Univ, Dept Math, Towson, MD 21252 USA
[2] Univ Bristol, Sch Math, Univ Walk, Bristol BS8 1TW, Avon, England
来源：
MONATSHEFTE FUR MATHEMATIK | 2017年 / 183卷 / 02期
关键词：
Waring-Goldbach problem; Vinogradov mean-value theorem; Weyl sums; MEAN-VALUE THEOREM; 4TH;
D O I：
10.1007/s00605-016-0936-7
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We apply recent progress on Vinogradov's mean value theorem to improve bounds for the function H(k) in the Waring-Goldbach problem. We obtain new results for all exponents , and in particular establish that for large k one has H(k) <= (4k - 2) log k - (2 log 2 - 1)k - 3.
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页码：303 / 310
页数：8
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