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ON A PROBLEM OF SUMS OF MIXED POWERS (II)
作者姓名:Lu Minggao  Yu Gang
作者单位:[1]DepartmentofMathematics,ShanghaiUniversity(JiadingCampus),Shanghai201800 [2]DepartmentofMathematics,UniversityofGeorgia,AthensGA30602
摘    要:ONAPROBLEMOFSUMSOFMIXEDPOWERS(I)LUMINGGAOYUGANGAbstractLetRb,c(n)denotethenumberofrepresentationsofnasthesumofonesquare,fo...

关 键 词:混合幂  渐进公式  Warings问题  变量
收稿时间:1994/7/20 0:00:00
修稿时间:1996/6/21 0:00:00

ON A PROBLEM OF SUMS OF MIXED POWERS (II)
Lu Minggao,Yu Gang.ON A PROBLEM OF SUMS OF MIXED POWERS (II)[J].Chinese Annals of Mathematics,Series B,1997,18(2):243-248.
Authors:Lu Minggao and Yu Gang
Institution:LU MINGGAO * YU GANG **
Abstract:Let $R_{b,c}(n)$ denote the number of representations of $n$ as the sum of one square, four cubes, one $b$-th power and one $c$-th power of natural numbers. It is shown that if $b=4$, $4\le c\le 35$, or $b=5, 5\le c\le 13$, or $b=6, 6\le c\le 9$, or $b=c=7$, then $R_{b,c}(n)\gg n^{5/6+1/b+1/c}$ for all sufficiently large $n$.
Keywords:Mixed power  Warings problem and variants  Asymptotic formulae
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