Detail publikace

Exact asymptotics of positive solutions to Dickman equation

Originální název

Exact asymptotics of positive solutions to Dickman equation

Anglický název

Exact asymptotics of positive solutions to Dickman equation

Jazyk

en

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

Anglický 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

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"
}