A note on the completeness of an exponential type sequence

被引：5
|
作者：
Fang, Jinhui [1 ]
机构：
[1] Nanjing Univ Informat Sci & Technol, Dept Math, Nanjing 210044, Peoples R China
来源：
CHINESE ANNALS OF MATHEMATICS SERIES B | 2011年 / 32卷 / 04期
基金：
中国国家自然科学基金;
关键词：
Complete sequence; Coprime; Residue;
D O I：
10.1007/s11401-011-0660-5
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
For any given coprime integers p and q greater than 1, in 1959, B. J. Birch proved that all sufficiently large integers can be expressed as a sum of pairwise distinct terms of the form p (a) q (b) . As Davenport observed, Birch's proof can be modified to show that the exponent b can be bounded in terms of p and q. In 2000, N. Hegyvari gave an effective version of this bound. The author improves this bound.
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页码：527 / 532
页数：6
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