Functional Equations Associated to Collatz-Type Maps on Integer Rings of Algebraic Number Fields
arXiv:2111.07882
Abstract
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 method to deal with not only a large class of Collatz-type maps defined on the integers, but further generalizations thereof to Collatz-type maps on the rings of integers on an arbitrary algebraic number field.
Withdrawn due to an error in section three, where the structure of the quotient of a ring of algebraic integers modulo an ideal thereof was not incorrectly described