Δ(x)的高次均值(Ⅳ) |
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引用本文: | 翟文广.Δ(x)的高次均值(Ⅳ)[J].数学学报,2006,49(3):639-646. |
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作者姓名: | 翟文广 |
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作者单位: | 山东师范大学数学科学学院 济南 250014 |
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基金项目: | 国家自然科学基金项目(10301038) |
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摘 要: | 研究了Dirichlet除数问题的余项Δ(x)在小区间上的k次积分均值(k≥3), 并得到了其渐近公式.特别在k=3和k=4时,进一步改进了Ivic和Sargos的结果.
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关 键 词: | Dirichlet除数问题 余项 积分均值 |
文章编号: | 0583-1431(2006)03-0639-08 |
收稿时间: | 2004-12-25 |
修稿时间: | 2004-12-252005-04-20 |
On Higher-Power Moments of Δ(x)(Ⅳ) |
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Institution: | Wen Guang ZHAI School of Mathematical Sciences, Shandong Normal University, Jinan 250014, P. R. China |
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Abstract: | Suppose Δ(x) is the error term of the Dirichlet divisor problem. In this paper we study the κth power moment of Δ(x) in short intervals for k≥3 and obtain its asymptotic formula. Especially when k=3 and k=4, we improve further the previous results of Ivic and Sargos. |
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Keywords: | Dirichlet divisor problem error term integral mean velue |
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