Frontiers of Mathematics in China >
DDT Theorem over square-free numbers in short interval
Received date: 23 Feb 2016
Accepted date: 06 May 2016
Published date: 20 Feb 2017
Copyright
We study the Cesàro means related to the divisor function. We show that the DDT Theorem holds over square-free numbers in short interval, which generalizes some results established by Deshouillers-Dress-Tenenbaum and by Cui-Wu.
Key words: Selberg-Delang method; arcsine law; square-free number
Bin FENG , Zhen CUI . DDT Theorem over square-free numbers in short interval[J]. Frontiers of Mathematics in China, 2017 , 12(2) : 367 -375 . DOI: 10.1007/s11464-016-0547-6
1 |
Cui Z, Wu J. The Selberg-Delange method in short intervals with an application. Acta Arith, 2014, 163(3): 247–260
|
2 |
Delange H. Sur les formules dues `a Atle Selberg. Bull Sci Math 2º série, 1959, 83: 101–111
|
3 |
Delange H. Sur les formules de Atle Selberg. Acta Arith, 1971, 19: 105–146
|
4 |
Deshouillers J-M, Dress F, Tenenbaum G. Lois de répartition des diviseurs, 1. Acta Arith, 1979, 23: 273–283
|
5 |
Hanrot G, Tenenbaum G, Wu J. Moyennes de certaines fonctions arithmétiques sur les entiers friables, 2. Proc Lond Math Soc (3), 2008, 96: 107–135
|
6 |
Lau Y-K. Summatory formula of the convolution of two arithmetical functions. Monatsh Math, 2002, 136(1): 35–45
|
7 |
Lau Y-K, Wu J. Sums of some multiplicative functions over a special set of integers. Acta Arith, 2003, 101(4): 365–394
|
8 |
Selberg A. Note on the paper by L. G. Sathe. J Indian Math Soc, 1954, 18: 83–87
|
9 |
Tenenbaum G. Introduction to Analytic and Probabilistic Number theory. Cambridge Studies in Advanced Mathematics, 46. Cambridge: Cambridge University Press, 1995
|
10 |
Tenenbaum G, Wu J. Moyennes de certaines fonctions multiplicatives sur les entiers friables. J Reine Angew Math, 2003, 564: 119–166
|
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