Exact asymptotics of positive solutions to Dickman equation

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26110%2F18%3APU128793" target="_blank" >RIV/00216305:26110/18:PU128793 - isvavai.cz</a>
Result on the web
<a href="http://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=14695" target="_blank" >http://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=14695</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.3934/dcdsb.2018007" target="_blank" >10.3934/dcdsb.2018007</a>

Result language
angličtina
Original language name
Exact asymptotics of positive solutions to Dickman equation
Original language description
The paper considers the Dickman equation. The number theory uses what is called a Dickman (or Dickman -de Bruijn) function, which is the solution to this equation defined by an initial function x(t)=1 if 0≤t≤1. The Dickman equation has two classes of asymptotically different positive solutions. The paper investigates their asymptotic behaviors in detail. A structure formula describing the asymptotic behavior of all solutions to the Dickman equation is given, an improvement of the well-known asymptotic behavior of the Dickman function, important in number theory, is derived and the problem of whether a given initial function defines dominant or subdominant solution is dealt with
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10102 - Applied mathematics

Project
<a href="/en/project/LO1408" target="_blank" >LO1408: AdMaS UP – Advanced Building Materials, Structures and Technologies</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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