• Corpus ID: 123741810

Some Analytic Aspects Concerning the Collatz Problem

  title={Some Analytic Aspects Concerning the Collatz Problem},
  author={G. Meinardus},
A series of relatively simple equivalences to the Collatz conjecture, concerning the Collatz mapping [...] are presented. [...] The main topic of this paper consists in investigating a certain linear equation in the space of special Dirichlet series. The conjecture that this equation possesses a null space of dimension 1, generated by the Riemann zeta function, is equivalent to the Collatz conjecture. A number of analytic properties of the operator, which defines the linear equation, is given… 
2 Citations

Conservation of Singularities in Functional Equations Associated to Collatz-Type Dynamical Systems; or, Dreamcatchers for Hydra Maps

It is known that the Collatz Conjecture (and the study of similar maps, here called "Hydra maps") can be stated in terms of solution sets of functional equations; or, equivalently, the fixed points

Functional Equations Associated to Collatz-Type Maps on Integer Rings of Algebraic Number Fields

In 1995, Meinardus & Berg presented a reformulation of the Collatz Conjecture in terms of a functional equation in a single complex variable over the open unit disk. This paper generalizes that



The Dynamical System Generated by the 3n+1 Function

Some ideas around 3n+1 iterations.- Analysis of the Collatz graph.- 3-adic averages of counting functions.- An asymptotically homogeneous Markov chain.- Mixing and predecessor density.

Über das Syracuse Problem

Einleitung: Das sog. 3n+1-Problem, auch Collatz-Problem oder Syracuse-Problem genannt, hat in der letzten Zeit an Aktualitat gewonnen. Eine Reihe von Ubersichtsartikeln macht dies deutlich. Die

Functional Equations Connected With The Collatz Problem

In this paper, some aspects of the famous 3n + 1 problem, due to L. Coilatz, are studied. Introducing generating functions for the iterated mappings, we derive certain linear recursion formulae and

Einführung in die analytische Zahlentheorie

Aqout the motivation of the (3n + 1) - problem

  • J. Qufu Nomen Univ. Nat. Sei
  • 1986

J ~ : Das Collatz - Problem . Publ . in : Mathematik - Lexikon , Bd . 1 , ed . G . Walz

  • The Dynamical System Generated by the 3 n + 1 Function , Lecture Notes in Math .

Meinardus : The 3n + 1 Collatz Problem and Functional Equations

  • Rostock Math. Koll
  • 1995