Publication detail

Exact asymptotics of positive solutions to Dickman equation

DIBLÍK, J. MEDINA, R.

Original Title

Exact asymptotics of positive solutions to Dickman equation

English Title

Exact asymptotics of positive solutions to Dickman equation

Type

journal article in Web of Science

Language

en

Original Abstract

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

English abstract

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

Keywords

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

Released

15.01.2018

Publisher

Americal Institute of Mathematical Sciences

ISBN

1553-524X

Periodical

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B

Year of study

23

Number

1

State

US

Pages from

101

Pages to

121

Pages count

21

URL

Documents

BibTex


@article{BUT149494,
  author="Josef {Diblík} and Rigoberto {Medina}",
  title="Exact asymptotics of positive solutions to Dickman equation",
  annote="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",
  address="Americal Institute of Mathematical Sciences",
  chapter="149494",
  doi="10.3934/dcdsb.2018007",
  howpublished="print",
  institution="Americal Institute of Mathematical Sciences",
  number="1",
  volume="23",
  year="2018",
  month="january",
  pages="101--121",
  publisher="Americal Institute of Mathematical Sciences",
  type="journal article in Web of Science"
}