A Necessary Condition on the Collatz Conjecture

TL;DR

This paper explores a necessary condition related to the Collatz conjecture, focusing on the convergence of a complex-valued function sequence under a linear operator, aiming to shed light on the conjecture's validity.

Contribution

It introduces a necessary condition involving complex functions and linear operators that must be satisfied for the Collatz conjecture to hold.

Findings

Identifies a specific necessary condition for the Collatz conjecture.

Connects the conjecture to complex function convergence.

Provides a new perspective on the conjecture's underlying structure.

Abstract

The Collatz conjecture implies that an iterated function sequence under a certain linear operator, beginning with a certain complex valued function, must converge to a certain complex function.