| THE FUNCTION dk（n） ATCONSECUTIVE INTEGERS |
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| 引用本文： | MENG Zaizhao. THE FUNCTION dk（n） ATCONSECUTIVE INTEGERS[J]. 数学年刊B辑(英文版), 1999, 20(4): 473-478 |
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| 作者姓名： | MENG Zaizhao |
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| 作者单位： | Department of Mathematics，Peking University，Beijing 100871，China |
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| 摘 要： | 51.IntroductionForallpositiveintegersk32,wedefinethefunctionsdk(n)bytheidentityWeknowthatdk(n)isamultiplicativefunction.Ifthestandardformofnisn=p?'p:'tthenwehavethefollowingformu1aTheaboveformulascanbefoundin[4].Inl984,Heath-Br.wnl2]showedthatforsufficientlylargex,#{nSx'd(n)=d(n 1)}>>x(logx)-'.(1.3)Inl987,Hi1debrand[31improvedthelowerboundto#{n5x:d(n)=d(n 1)}>>x(loglogx)-'.(1.4)Inthispaper5weprovethefollowingresult.Theorem.Smposek(22)isapositiveinteger.FOrsopcientlylarpex,#Ak(x):=#{nS…
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| 关 键 词： | 除数函数 乘法函数 余同方程 连贯整数 |
| 收稿时间： | 1998-03-13 |
| 修稿时间： | 1999-05-19 |
THE FUNCTION dk(n)ATCONSECUTIVE INTEGERS |
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| MENG Zaizhao. THE FUNCTION dk(n)ATCONSECUTIVE INTEGERS[J]. Chinese Annals of Mathematics,Series B, 1999, 20(4): 473-478 |
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| Authors: | MENG Zaizhao |
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| Affiliation: | DepartmentofMathematics,pekingUniveraitcaBeijing100871,China. |
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| Abstract: | Let dk(n) denote the k-fold iterated divisor function |
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| Keywords: | Divisor function Multiplicative function Congruence |
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