Waring's problem for sixteenth powers

被引:0
|
作者
李红泽
机构
[1] China
[2] Jinan 250100
[3] Shandong University
[4] Department of Mathematics
基金
中国国家自然科学基金;
关键词
Waring’s problem; iterative method; estimation of exponential sum;
D O I
暂无
中图分类号
O152 [群论];
学科分类号
070104 ;
摘要
Let G (k) denote the smallest s such that every sufficiently large natural number is the sum of at most s fcth powers of natural numbers. It is proved that G (16)<111. This improves the result of T. D. Wooley’s.
引用
收藏
页码:56 / 64
页数:9
相关论文
共 50 条
  • [21] On the Waring-Goldbach problem for seventh powers
    Kumchev, AV
    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2005, 133 (10) : 2927 - 2937
  • [22] Waring-Goldbach Problem for Unlike Powers
    Xiu Min REN
    Kai Man TSANG
    ActaMathematicaSinica(EnglishSeries), 2007, 23 (02) : 265 - 280
  • [23] An improvement on Waring–Goldbach problem for unlike powers
    Zhixin Liu
    Acta Mathematica Hungarica, 2011, 130 : 118 - 139
  • [24] On the easier waring problem for powers of primes I
    Erdos, P
    PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 1937, 33 : 6 - 12
  • [25] On Waring-Goldbach problem for unlike powers
    Li, Jinjiang
    Zhang, Min
    INTERNATIONAL JOURNAL OF NUMBER THEORY, 2018, 14 (06) : 1669 - 1687
  • [26] On Waring-Goldbach problem of mixed powers
    Lu, Xiaodong
    Mu, Quanwu
    JOURNAL DE THEORIE DES NOMBRES DE BORDEAUX, 2016, 28 (02): : 523 - 538
  • [27] On the Waring Goldbach problem for eighth and higher powers
    Kumchev, Angel V.
    Wooley, Trevor D.
    JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 2016, 93 : 811 - 824
  • [28] The asymptotic formula in Waring’s problem for one square and seventeen fifth powers
    Jörg Brüdern
    Koichi Kawada
    Monatshefte für Mathematik, 2011, 162 : 385 - 407
  • [29] The asymptotic formula in Waring's problem for one square and seventeen fifth powers
    Bruedern, Joerg
    Kawada, Koichi
    MONATSHEFTE FUR MATHEMATIK, 2011, 162 (04): : 385 - 407
  • [30] Waring’s Theorem for Binary Powers
    Daniel M. Kane
    Carlo Sanna
    Jeffrey Shallit
    Combinatorica, 2019, 39 : 1335 - 1350