DDT Theorem over square-free numbers in short interval

Bin FENG; Zhen CUI

doi:10.1007/s11464-016-0547-6

Front. Math. China ›› 2017, Vol. 12 ›› Issue (2) : 367 -375. DOI: 10.1007/s11464-016-0547-6

RESEARCH ARTICLE

DDT Theorem over square-free numbers in short interval

Bin FENG ¹^,²^,^†
, Zhen CUI ¹

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Abstract

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.

Keywords

Selberg-Delang method / arcsine law / square-free number

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Bin FENG, Zhen CUI. DDT Theorem over square-free numbers in short interval. Front. Math. China, 2017, 12(2): 367-375 DOI:10.1007/s11464-016-0547-6

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References

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[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