Detail publikace

Exact asymptotics of positive solutions to Dickman equation

DIBLÍK, J. MEDINA, R.

Originální název

Exact asymptotics of positive solutions to Dickman equation

Typ

článek v časopise ve Web of Science, Jimp

Jazyk

angličtina

Originální abstrakt

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

Klíčová slova

Dickman equation; positive solution; dominant solution; subdominant solution; large time behavior; asymptotic representation; delayed differential equation.

Autoři

DIBLÍK, J.; MEDINA, R.

Vydáno

15. 1. 2018

Nakladatel

Americal Institute of Mathematical Sciences

ISSN

1553-524X

Periodikum

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B

Ročník

23

Číslo

1

Stát

Spojené státy americké

Strany od

101

Strany do

121

Strany počet

21

URL

http://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=14695

BibTex

@article{BUT149494,
  author="Josef {Diblík} and Rigoberto {Medina}",
  title="Exact asymptotics of positive solutions to Dickman equation",
  journal="DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B",
  year="2018",
  volume="23",
  number="1",
  pages="101--121",
  doi="10.3934/dcdsb.2018007",
  issn="1553-524X",
  url="http://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=14695"
}