Positive solutions to Dickman equation
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26220%2F16%3APU119322" target="_blank" >RIV/00216305:26220/16:PU119322 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Alternative languages
Result language
angličtina
Original language name
Positive solutions to Dickman equation
Original language description
We consider the Dickman equation x' (t)=-1/t x(t-1), for t go to infty. The number theory uses what is called a Dickman (or Dickman - de Bruin) 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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Classification
Type
D - Article in proceedings
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
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Continuities
S - Specificky vyzkum na vysokych skolach
Others
Publication year
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Article name in the collection
7th Podlasie Conference on Mathematics
ISBN
978-83-7431-478-7
ISSN
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e-ISSN
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Number of pages
2
Pages from-to
15-16
Publisher name
University of Bialystok, Pland
Place of publication
Bialystok
Event location
Bialystok
Event date
Jun 8, 2016
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
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