Mean values of the error term with shifted arguments in the circle problem

被引：0
|
作者：
Furuya, Jun [1 ,2 ]
Tanigawa, Yoshio [3 ]
机构：
[1] Hamamatsu Univ, Sch Med, Dept Integrated Human Sci Math, Higashi Ku, Handayama 1-20-1, Hamamatsu, Shizuoka 4313192, Japan
[2] Okinawa Natl Coll Technol, Dept Integrated Arts & Sci, Nago, Okinawa 9052192, Japan
[3] Nagoya Univ, Grad Sch Math, Nagoya, Aichi 4648602, Japan
来源：
NOTES ON NUMBER THEORY AND DISCRETE MATHEMATICS | 2014年 / 20卷 / 02期
关键词：
The circle problem; Mean value of error terms; Shifted sum; Bernoulli polynomial;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we show the relation between the shifted sum of a number-theoretic error term and its continuous mean (integral). We shall obtain a certain expression of the shifted sum as a linear combination of the continuous mean with the Bernoulli polynomials as their coefficients. As an application of our theorem, we give better approximations of the continuous mean by a shifted sum.
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页码：44 / 51
页数：8
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