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The Convolution Powers of the Dickman Function

 

作者: Douglas Hensley,  

 

期刊: Journal of the London Mathematical Society  （WILEY Available online 2016）
卷期: Volume s2-33, issue 3  

页码: 395-406

 

ISSN:0024-6107

 

年代: 2016

 

DOI:10.1112/jlms/s2-33.3.395

 

出版商: Oxford University Press

 

数据来源: WILEY

 

摘要:

There is a family of functionswα(u), 0<α<∞, related to the Dickman function ρ(u) by the relationsw1=e−γρ(u),wα∗wrβ=wα+rβ(u). We consider the analytic properties of thewα(u) and obtain an asymptotic formula forwα(u) valid uniformly in α ⩾ ε,u+α → ∞. Thewα(u) are of direct interest in number theory as well as for their connection to the Dickman function.

 

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